Arc pair grammar 0691082707

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Arc Pair Grammar

Arc Pair Grammar

David E. Johnson Paul M. Postal

PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY

Copyright © 1980 by Princeton University Press Published by Princeton University Press, Princeton, New Jersey In the United Kingdom: Princeton University Press, Guildford, Surrey ALL RIGHTS RESERVED

Library of Congress Cataloging in Publication Data will be found on the last printed page of this book Clothbound editions of Princeton University Press books are printed on acid-free paper, and binding materials are chosen for strength and durability Printed in the United States of America by Princeton University Press, Princeton, New Jersey

CONTENTS Preface

ϊχ

Chapter 1. Introduction 1.1. Sentences, Rules, and Grammars 1.2. Informal View of Sentences 1.3. Recent Historical Antecedents of APG 1.4. Intermezzo on Linguistic Theory 1.5. Notation and Technical Symbols

3 9 15 19 25

Chapter 2. Graph-Theoretic Aspects of APG 2.1. Primitives and Basic Defined Sets 2.2. Three Notions of "Arc" 2.3. Interpretation of Incomplete Arcs and Arcs 2.4. Properties of Arcs and Sets of Arcs 2.5. R-graphs 2.6. Notational Points

29 33 37 39 50 56

Chapter 3. Arc Pair Relations 3.1. Introduction to the Sponsor and Erase Relations 3.2. Self-Sponsorship and Self-Erasure 3.3. Examples and Discussion

60 64 66

Chapter 4. Pair Networks 4.1. S-graphs 4.2. L-graphs 4.3. Formal Definition of "PN"

75 91 101

Chapter 5. Basic Sponsor and Erase Laws 5.1. Successors and Predecessors 5.2. Replacers and Replacees 5.3. Successor, Replace, and Three Basic Erasure Laws 5.4. General Properties of Successor and Replace 5.5. A Fundamental Arc Typology 5.6. A Further Arc Typology

105 107 112 115 131 141

Chapter 6. Coordinate Determination 6.1. Preliminary Discussion 6.2. Domestic Arc Coordinate Determination 6.3. Immigrant Arc Coordinate Determination 6.4. Graft Coordinate Determination 6.5. The Fall-Through Law 6.6. An Alternative View of Coordinates

149 151 158 164 171 186

ν

vi

CONTENTS

Chapter 7. Focus on Clause Structure 7.1. Comments 7.2. Grammatical Categories and Constituents 7.3. Partially Lawful Determination of Node-Labeling 7.4. Some Properties of Basic Clauses: Predicates 7.5. Some Properties of Basic Clauses: Nominals 7.6. Overlay Arcs and Clause Structure

189 189 193 211 225 259

Chapter 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 8.7. 8.8.

8. Cho Arcs The Temporary Chomeur Condition Cosponsorship of Domestic Cho Arcs The Chomeur Law The Stratal Compactness Law The Stratal Uniqueness Theorem Clause Unions and The Chomeur Law Postscript 1: Partially Alternative Views of Cho Arcs Postscript 2: The Sponsors of Domestic Cho Arcs

272 289 295 310 316 323 356 357

Chapter 9.1. 9.2. 9.3. 9.4. 9.5. 9.6.

9. Further Principles Governing the Distribution of Cho Arcs The Problem 359 Constraints on Zeroing 360 A Constraint on Arcs Headed by UN Nodes 367 Remarks on O Nodes 390 Constraints on Members of Inexplicit 396 Postscript: Further Members of Inexplicit 398

Chapter 10.1. 10.2. 10.3. 10.4. 10.5. 10.6.

10. Ghost Arcs and Dummy Nominals Background 401 Ghost Arcs 403 The Basic Constraint on Ghost Arcs 405 Constraints on Ghost Arc Sponsors and Dummy Arcs 428 Cho Arc Types and A Further Characterization of Cho Arcs 438 Further Properties of Dummy Nominals 444

Chapter 11. Replacers and Anaphora 11.1. Basics 11.2. Arc Antecedence 11.3. Anaphoric Chains 11.4. Constraints on Cosponsors of Anaphoric Replacements 11.5. Forerunners and An Objection 11.6. Two Types of Anaphoric Connection 11.7. Further Remarks on Kernel Anaphoric Arcs 11.8. Parallelisms Between Coreferential Arcs and Copy Arcs 11.9. Constraints on Internal Survivors 11.10. Appendix: Ghost Arcs and Pro Arcs

448 456 465 476 479 483 501 506 519 545

Chapter 12.1. 12.2. 12.3. 12.4.

547 550 553 556

12. Linear Precedence Introductory Remarks LP Arc Basics Quasi-Rooted LP Arcs D-Sponsored LP Arcs

CONTENTS

12.5. Further Constraints on LP Arcs 12.6. LP Arcs and French Liaison 12.7. Surface Strings 12.8. A More Realistic View of Phonological Nodes 12.9. Further Remarks on Word Order 12.10. Another Conception of Linear Precedence in APG 12.11. A Still Different APG Approach to Linear Precedence Chapter 13.1. 13.2. 13.3. 13.4. 13.5. 13.6. 13.7.

13. Grafts, Pioneers, and Closures PrepositionalFlagging Upper and Lower Pioneers Case Marking Stranded Prepositions FlagDetermination Appendix 1: Proofs Appendix 2: Weakening the Immigrant Local Sponsor Law

Chapter 14.1. 14.2. 14.3. 14.4. 14.5. 14.6.

14. APG Rules and Grammars Preliminary Remarks PN Well-Formedness and Grammatical Rules Some Theoretical Implications of the APG View of Rules Remarks on Languages, Grammars, Rules, and Corpora The Unique Eraser Law and Grammatical Rules Further Universal Conditions Permitting Underspecification in Rules 14.7. The R-Sign Cho and Grammatical Rules

vii

565 568 578 585 592 596 600 602 611 622 638 642 651 653 655 656 661 677 687 704 711

References

715

Index

724

PREFACE The present volume is unusual in several respects. It presents in great detail a largely novel, formalized theory of linguistic structure. Al­ though we attempt to motivate and explain the various "properties and assumptions of the theory, and to illustrate their application in a variety of cases, this work provides little in the way of empirical support for the theory in question. There are several reasons for this. First, the theory presented is sufficiently complicated and developed to such a degree that even an incomplete presentation and description of its structure requires hundreds of pages. Serious attention to questions of empirical justifica­ tion would thus have expanded the work beyond all practical limits. Secondly, many (but by no means all) of the assumptions made in the pres­ ent theory are, we believe, justified by the results of the past five years of work in relational grammar (RG), work which formed the underpinnings and original motivation for the development of the present framework. Thirdly, the theory developed in the chapters to follow is sufficiently gen­ eral, broad, and detailed that its overall empirical testing is a massive job. It follows that this must be approached piecemeal. Our intention is, therefore, over a period of time to produce individual empirical works bearing on the ideas developed here. Although we have not provided much detailed empirical argumentation for various assumptions, we have, at key points, stressed the controversial character of our assumptions, cited opposing or contrasting viewpoints, and occasionally considered alternatives. In short, what is presented is not some minor idea embedded within familiar assumptions nor any modification of any current ideas or concep­ tions about grammar, but rather the basis for a new and different way of

X

PREFACE

conceptualizing grammatical phenomena. Developing such a framework in the detail attempted here is, as the reader will soon perceive, a sufficient­ ly laborious task that it necessarily limits the amount of empirical discus­ sion possible at this introductory stage. A notable feature of the present work, especially as compared to the norm in linguistic discussion, is its degree of formality. We have taken pains to state our assumptions formally, permitting proofs of a large num­ ber of theorems. This contributes, certainly, to making the reading of the work less facile than it might otherwise be. But we are convinced that no serious theory of grammar at this stage can avoid the necessity of true precision, which is, in linguistics today, a value widely praised but seldom instantiated. Without a precise and explicit statement of theories, it is impossible to know what they claim, thus impossible to confirm or disconfirm them. We have again and again had the experience of assuming that such and such was a (logical) consequence of our assumptions, only to find that it was not when we actually tried to construct a proof of the assumed truth in question. That is, we have found over and over that the technique of constructing formal proofs, only made possible by a formali­ zation of the underlying laws and definitions, is a highly productive and insight-yielding procedure. When one speaks about consequences of lin­ guistic assumptions, it is extremely difficult to eliminate as premises all sorts of background assumptions, unquestioned views, etc. It is only by actually proving a consequence on the basis of a fixed set of precise assumptions that one can be sure that its truth is guaranteed by the truth of those assumptions, and those alone. As a consequence, since linguis­ tic discussion is, currently, in general not of this character, we cannot avoid considerable skepticism with respect to those all too ubiquitous claims that such and such are consequences of view V, or that V explains this or that, when V has not been presented explicitly or precisely and when the purported consequences have not been proved (but just asserted) to follow from them.

PREFACE

xi

We can put the matter slightly differently as follows. The term "theory" occurs frequently in linguistics, and there are, if one judges by the use of this term, a variety of partially or totally different grammatical theories available today. However, it turns out that what are called theo­ ries are almost invariably collections of differentially vague, partially de­ veloped or undeveloped ideas. Even highly prestigious collections of ideas do not consist of explicit sets of precise assumptions. And, to the extent that they do not, it is impossible to determine their consequences, and hence to study their truth or falsity. The deleterious consequences of imprecision and inexplicitness in linguistic work are sufficiently great, in fact, so enormous, that the practical difficulties imposed (far more, note, on the developers of a genuine theory than on its consumers) are minor in comparison with the virtues. These, at any rate, are the assumptions which have led us to seek the unusual degree of explicitness and preci­ sion found in what follows. A final note. We have cited methodological grounds justifying the need for precise formulations of linguistic theories. We suspect, however, that one important reason why it has been possible in this study to reach, with a reasonably limited effort (approximately two man years), a serious level of formalization is connected to the nature of the ideas being formal­ ized. There is a sense in which these ideas are natural, simple, general, etc.—that is, a sense in which they lend themselves very directly to formal­ ization and, moreover, to a formalization of a rather elementary kind, making use of only quite standard and limited logico-mathematical appara­ tus. It is not unreasonable to assume that this kind of success, notably not duplicated in other frameworks, if combined with broad empirical coverage and adequacy, is a measure of the truth of the underlying assumptions. In preparing this work, we have benefited from innumerable past dis­ cussions with, and insights of, D. M. Perlmutter, to whom we would like to express our appreciation. Other.useful suggestions from J. Johnson,

xii

PREFACE

G. Lakoff, W. Marsh, P. Neubauer, W. Plath, G. K. Pullum, A. Radford, L. Zgusta, and two anonymous readers are also gratefully acknowledged. We are also extremely grateful to M. Gross for checking, and in some cases improving, the French examples cited. It goes without saying that responsibility for all remaining errors, inaccuracies, etc., rests entirely with the authors. D. E. Johnson is very grateful to The National Endowment for the Humanities for supporting his work on this project through a Fellowship for Independent Study and Research (#F77-77). He would also like to ex­ press his appreciation to the IBM Thomas J. Watson Research Center for graciously making their facilities open to him during the year 1977.

Arc Pair Grammar

CHAPTER 1 INTRODUCTION 1.1. Sentences, rules, and grammars Any linguistic theory must involve two basic interrelated conceptions. First, there must be a set of ideas about the nature of the basic elements of language, sentences.1 Any such theory must have a basic conception of what kind of formal objects sentences are. For example, in all current variants of transformational theory (henceforth TG), sentences are regard­ ed as quite complicated formal objects involving logical representations, phonological and phonetic representations, and a central core of structure called a derivation, which consists of a sequence of graph-theoretic ob­ jects called (not too happily) constituent structure trees.2 Secondly, a linguistic theory must have a conception of what a possible sentenceSpecifying system or grammar is. This necessarily involves views about what a possible grammatical rule is, what a possible combination of gram­ matical rules (possible grammar) is, and a specification of how grammars

We use "sentence" here in the widest, most general sense. In Chapter 4, we show that the notion PN defined there is sufficiently broad that two or more "surface sentences" can correspond to a single PN. For the most part, we ignore complications that this entails. That is, we use "sentence" ambiguously to refer both to the total real world structure represented by a PN, and to the individual elements called "sentences" in usual linguistic discourse. Hence with respect to: (i) There's a gorilla. He is unhappy. there is one sense of "sentence" in which (i) is a single sentence, i.e., repre­ sents a single PN, and another in which it involves two sentences. 2 The phrase markers of TG discussions are unhappily called trees because the relevant notion differs from the standard graph-theoretic notion tree. See Chapter 2.

4

1. INTRODUCTION

characterize classes of sentences. Inevitably, the conception of the nature of a sentence will greatly determine what conception of grammati­ cal rule is required, although the notion of rule adopted may (and normally will) feed back and determine in part the conception of linguistic object. Thus, it is the idea that grammatical structure involves a sequence of con­ stituent structures (rather than the single structure of structuralist theories) which leads transformational theorists to a conception of grammatical rule countenancing grammatical transformations, etc. But the presumption that transformations exist has, in turn, led to many assumptions about sentence structure, e.g., that there are symbols which trigger transformations, ele­ ments like doom, traces, etc. 3 As will become clear, the current work makes no use of the fundamental TG construct Derivation and a fortiori no use of those concepts dependent on or related to this central notion. This work develops a new conceptual framework, which we call Arc Pair Grammar (henceforth: APG). APG is radically different from any other extant conception of linguistic theory along many but not all parame­ ters. Although its concept of sentence structure is an outgrowth of largely unpublished work in RG (see section 1.3 for discussion of the recent his­ torical antecedents of APG), APG will be about 95 percent new even to those familiar with work in RG. To those unfamiliar with the RG frame­ work, APG will be essentially 100 percent novel. Let us briefly contrast one current TG framework with that of APG. Within the current version of the so-called extended standard theory (of TG), a grammar is characterized in terms of various types of object, inter alia (see Chomsky and Lasnik [1977]): (i) a base containing a categorial component (context-free grammar generating an infinite set of phrase

Both doom (see Postal [l 97θ]) and traces are, like global devices in gen­ eral, designed to overcome a basic deficiency built into the most basic assump­ tions of TG theory, namely, the fact that transformational applications destroy or "lose" information, information which is necessary even after it is "lost." This problem cannot arise in APG terms, since no information is, or ever could be, "lost."

1.1. SENTENCES, RULES, AND GRAMMARS

5

markers) and a lexicon (containing word formation and lexical redundancy rules); (ii) lexical insertion rules; (iii) a transformational component; (iv) a semantic interpretive component; (v) a deletion component; (vi) a surface filter component; (vii) a phonological interpretive component, and (viii) a stylistic component. 4 Corresponding to this TG view of a grammar, sen­ tence structure involves various levels of representation, roughly: (a) an initial phrase marker generated by (i); (b) a base phrase marker, generated by (ii); (c) a sequence of phrase markers or a derivation, generated by (iii), the last phrase marker being termed a surface structure, determined in part to be well-formed by (vi); (d) a logical form, generated by (iv); (e) a level determined by the output of (v); (f) a phonological form, generated by (vii), and (g) a final output generated by (viii). In contrast, APG represents each natural language sentence in terms of a formal object called a Pair Network (PN). A PN is, from one view­ point, a system involving four components: (i) an overall graph-theoretic object called a Relational Graph (R-graph), discussed in detail in Chapter 2; (ii) a graph-theoretic object which is a subpart of the overall R-graph in (i), called a Logical Graph (L-graph), discussed in detail in Chapter 4; (iii) a graph-theoretic object which is a subpart of the overall R-graph in (i) and distinct from the L-graph, called a Surface Graph (S-graph), also discussed in detail in Chapter 4; and (iv) two primitive relations called Sponsor and Erase, ranging over pairs of elements (called arcs) from R-graphs. These are discussed throughout this work from Chapter 5 on. 5

^Actually, it is impossible to consider seriously notions like "semantic interpretive component," "stylistic component," "rules of construal," and re­ lated ideas mentioned in Chomsky and Lasnik (1977), for no precise account of these is given there or anywhere else to our knowledge. We note the almost cava­ lier disregard for the need for explicitness and precision which surrounds these and other notions in this and other related work of recent vintage. On the need for precision and explicitness in grammatical work, see Dougherty (1972, 1973). 5 Due to practical limitations, it has not proved possible to consider in any serious way the question of an APG approach to phonology. As a consequence, at a few places, the current development, which ignores phonology, is quite un­ realistic in certain respects (particularly, those involving the specification and

6

1. INTRODUCTION

The APG construct L-graph is a formal characterization of the notion (linguistically motivated) logical form. The construct S-graph is roughly the formal characterization within APG of that aspect of sentence struc­ ture characterized in terms of Surface Structure in TG. The relations Sponsor and Erase and the laws and grammatical rules which refer to them are the APG explication not only of that aspect of sentence structure characterized in TG in terms of derivations and conditions on derivations, but also that aspect putatively characterized by interpretive components, stylistic components, etc. In short, the APG conception of grammar is far more homogeneous and monolithic than that of TG. It claims that there is a single web of notions relevant for describing all aspects of language, a claim in no way inconsistent with the existence of differentiating fea­ tures of various subaspects. Thus, within APG there is no notion of, e.g., base component, lexical component, lexical insertion rules, transforma­ tional component, semantic interpretive component, deletion component, surface filter component, stylistic component, nor any of the other or associated constructs (cycles, rule ordering, traces, etc.) commonly assumed to be characterized in terms of, or held to apply to, the preceding aspects of TG. A PN is simply a pairing of a Sponsor relation and an Erase relation such that (i) each relation is a set of ordered pairs of arcs, and (ii) the set of arcs formed by the domains and ranges of Sponsor and Erase (a) forms an R-graph and (b) has two subsets, one forming an L-graph and one forming an S-graph. Thus, R-graph, L-graph, and S-graph are deriva­ tive concepts, part of the defining criteria of the single formal objects called PNs. Corresponding to the fundamental difference between the TG and APG notions of sentence structure are differences in the associated notions of

interpretation of the class of so-called phonological nodes in Chapter 2). We be­ lieve that ultimately a theory of phonology embedded within APG assumptions will prove possible. We touch on these matters more concretely in section 7 of Chapter 12.

1.1. SENTENCES, RULES, AND GRAMMARS

7

grammatical rule and grammar. Unlike, e.g., transformations and other TG rules, APG grammatical rules do not map formal objects into formal objects via a specified set of operations. Rather, APG rules, like the laws of APG universal grammar (PN laws), check for the cooccurrence or noncooccurrence of specified properties of given PNs. More specifically, both PN laws and all APG grammatical rules are interpreted as material implications in the standard logical sense. Thus, APG draws it rules

from this intensively studied and antecedently (to linguistic work) formally characterized class of objects. The essential difference between APG grammatical rules and PN laws is one of scope. The former are languageparticular and thus not necessarily an aspect of any particular language. Thus PN laws are material implications which determine well-formedness in all languages; grammatical rules are material implications which deter­ mine well-formedness only for individual languages. Because of this inter­ pretation of rules adopted in APG, notions like cycles, rule ordering, etc., so much discussed in the TG literature, are necessarily excluded from consideration. More precisely, a grammar in APG terms for some language L a is the union of the set of APG PN laws with some finite set of languageparticular material implications specific to L a . The set formed by this union is unstructured in the sense of containing no components. Roughly (see Chapter 14), a given PN is well formed with respect to L a just in case it model-theoretically satisfies the grammar of L a , which is the union of the set of PN laws with those material implications particular to L a . Hence the APG conception of grammar differs from, e.g., the TG con­ ception, as radically as do the APG conceptions of sentence structure and individual grammatical rule. The negative idea of representing sentence structure in terms of ob­ jects not having derivations as subcomponents is not unique to APG. For example, RG as conceived most recently by Perlmutter and Postal (see Perlmutter and Postal [1977], Postal [1977], and below), Lakoff's (1977) conception of linguistic gestalts, and Hudson's (1976) idea of daughter

8

1. INTRODUCTION

dependency grammar, among others, all share the vague, unformalized and negative assumption that no aspect of sentence structure is properly char­ acterized in terms of derivations. Since the above approaches to sentence structure all reject derivations, they could, in contrast to all variants of TG, be referred to as "uninetwork theories." However, the formal objects positively assumed in these views are considerably different in each case. The rest of this work is devoted to elaborating the concept PN, and, to a much lesser degree, the notions of grammatical rule and grammar which go with it. In this volume, we proceed inductively, specifying the primitive concepts we assume and then building up to formal definitions of "R-graph," "S-graph," "L-graph," and "PN," (Chapters 2-4). Subse­ quently, we motivate and formalize a large set of PN laws which are designed to characterize (at the level of APG universal grammar) the notion Possible PN (see Chapters 5-13). These laws, plus the definition of "PN," characterize the concept Genetic PN (see Chapter 14, section 1). These are PNs which satisfy all PN laws and thus are well formed at the level of universal grammar, though not necessarily in any particular language. Finally, we discuss briefly the APG notions of Grammatical Rule, Grammar, and Well-Formed PN (for language L a ). It is our working hypothesis that ultimately the entire syntactic, se­ mantic, pragmatic, and phonological organization of a sentence is correct­ ly formalized in terms of PNs. Our studies so far have concentrated on areas traditionally called syntactic. Nonetheless, one or two basic in­ sights have emerged which have consequences for the representation of semantic or logical form. These mostly involve the area now usually dis­ cussed under the rubric "coreference" (see Chapter 11), but also other matters (see the discussion of The L-graph No Circuit Condition in Chapter 4). In addition, we believe the notion PN provides the correct mechanisms for relating logical form and superficial syntactic structure, embedding this in the same conception that relates different" aspects of syntactic structure to each other.

1.2. INFORMAL VIEW OF SENTENCES

9

1.2. Informal view of sentences Our basic conception of human language at the most abstract level does not, naturally, differ from that of other generative views. We take a language to be simply an infinite, presumed recursively enumerable, set of elements of some type, called sentences. From another point of view, we regard a language as essentially characterizable by a finite formal object, a grammar, which specifies the membership of the set of sentences. As noted earlier, "sentence" in this sense is not to be identified with a string of words or morphemes, 6 but rather refers to the entire grammatical organization in the widest sense. Thus sentences are highly complex formal objects of some sort. Our informal conception of sentence is this. A sentence involves a set of primitive linguistic elements; a set, PGR, of primitive grammatical relations holding between linguistic elements; a set of linguistic levels, which stratify the grammatical relations into distinct linguistic states; and, most characteristically, two primitive, binary relations called Sponsor and Erase, which hold between (in some cases, unary) sequences of lin­ guistic states. The relation Sponsor organizes subsets of linguistic states into chains, defining sequences of distinct statuses for the primi­ tive linguistic elements bearing the grammatical relations holding at various linguistic levels. In terms of Sponsor, it is possible to define, inter alia, two relations, Successor and Replace, which play distinct, fundamental roles in APG. A simple example should help clarify the fore­ going abstract description of our view. Consider: (1) Max was jostled by Naomi. Oversimplifying considerably for expository purposes, (1), under our in­ formal view, has the following partial structure. The primitive elements of (1) include a nominal, Max, a nominal, Naomi, and a clause correspond^That is, we see no need to say that something like: (i) The students are revolting. represents one sentence with two structures, or the like. In our terms, (i) repre-

10

1. INTRODUCTION

ing to the entire sentence. The structure of (1) involves two linguistic levels. At the first level (L1), Max bears the direct object relation, and Naomi bears the subject relation, to the clause. At the second level (L2), Max bears the subject relation, and Naomi bears the chomeur relation, to the clause. With respect to clause structure, (1) involves four linguistic states: (Si) Max bearing the direct object relation to the clause at L1 , (S2) Naomi bearing the subject relation to the clause at L 1 , (S3) Max bearing the subject relation to the clause at L2 , and (S4) Naomi bearing the chomeur relation to the clause at L2 . In terms of the Sponsor relations of relevance here,

(Si) sponsors (S3) and (S2) sponsors (S4). More

specifically, these two sponsor relation pairs are of the Successor type (for further discussion, see Chapters 3 and 5). (S3) is the successor of (Si), and (S4) is the successor of (S2). Further, ignoring passive verbal morphology and the auxiliary, L 1 and L 2 "contain" a verb, jostled, which bears the predicate relation to the clause, defining two more states. Diagrammatically:

(S3)

subject at Lg of

(2)

direct object at L| of

Max

Clausex (S4)

chomeur at Lo of

Naomi Of subject at Li of

(was) jostled

(S5)

(S6)

at L, of

predicate at Lg of

sents two distinct PNs which happen to define the same surface string (defined in section 7 of Chapter 12). 7

We ignore here sponsor relations where a given state sponsors itself, e.g., we regard (Si) and (S2) as self-sponsoring. This correlates with the fact that these two strata are relevant to the determination of the meaning of the sentence, while nonself-sponsoring states, e.g., (S3) and (S4) are not (see Chapters 3 and 4).

1.2. INFORMAL VIEW OF SENTENCES

11

Notice that there is no sponsor relation between thie two states: (S5) jostled bearing the predicate relation to the clause in L 1 and (S6) jostled bearing the predicate relation to the clause in L 2 . The defined relation Replace is relevant to our account of: (3) Max knows himself. Again oversimplifying greatly, (3), under our informal view, has the follow­ ing partial structure. The primitive elements of (3) include two nominals, Max and himself, and a verb, knows, in addition to a clause. As in the case of (1), (3) involves two linguistic levels. Level I(L 1 ) has the following makeup: Max bears both the subject and direct object relations, and knows bears the predicate relation, to the clause. Level 2 (L 2 ), in contrast, has the following character: Max bears the subject relation, himself bears the direct object relation, and knows bears the predicate re­ lation, to the clause. Thus the structure of (3) involves the following six linguistic states: (Si) Max bearing the subject relation to the clause at L 1 ; (S2) Max bearing the direct object relation to the clause at L 1 ; (S3) knows bearing the predicate relation to the clause at L 1 ; (S4) Max bear­ ing the subject relation to the clause at L 2 ; (S5) himself bearing the direct object relation to the clause at L 2 ; (S6) knows bearing the predi­ cate relation to the clause at L 2 . In terms of the Sponsor relations of relevance here, (S2) sponsors (S5). This pair determines a defined rela­ tion called Replace, i.e., (S5) replaces (S2). Diagrammatically: (4)

(S4) subject ot Lg of

(Si)

subject at L| of

(S2) direct object ot L| of

I

(S5) direct object at 1-2 of

(S3) predicate at L| of knows

(S6) predicate at L2

Clause.

12

1. INTRODUCTION

Note that there is no sponsor relation between (Si) and (S4) nor between (S3) and (S6). The role of linguistic levels in sentences is rather analogous to the role of time or temporal points in the description of real world events and states. Just as it is vague to say, in the domain of social relations, that two individuals, a, b, are married (in a state of marriage), it is vague to say that two linguistic elements bear some relation. Rather, one should say that a, b are married at point t in time or over some interval of points in time, and that two linguistic elements stand in some relation at some level (though they may not be in that relation or any other relation at others). A linguistic state is thus a specification that a pair of ele­ ments are in a fixed relation at a fixed level. The primitive Sponsor rela­ tion means that there are fixed transitions between nontrivially distinct linguistic states, i.e., states which do not differ just in terms of level specification.

Q

For example, if a particular element enters into three

states at three different levels, it is, under fixed conditions, possible to specify a unique ordering (a sponsor chain) among these. For instance, one linguistic state might specify that a linguistic element, a, bears the indirect object relation to a second element, b; a successive state could specify that a and b are related by the direct object relation; and a third might specify that a and b are related by the subject relation. The three linguistic states alone indicate only which relations hold at which levels. It is the sponsor chain which indicates the order of transition from one state to a nontrivially distinct state, determining which is the first state, which the last, etc., among a group of related states. This is im­ portant, since first states, last states, etc., determine lawfully which in­ formation is relevant for the semantic structure of sentences, which for the phonetic structure, etc. In particular, we assume that the set of linguistic states in a sentence permits a definition in general terms of two distinct subsets of states, one g

For example, the states Subject (a,b) at L 3 and Subject (a,b) at L 4 are trivially distinct since they differ only in the specification vs. L 4 . In con­ trast, Subject (a,b) at and Direct Object (a,b) at L 4 are nontrivially distinct.

1.2. INFORMAL VIEW OF SENTENCES

13

characterizing the logical or semantic structure of the sentences, the other characterizing the directly phonologically relevant aspect of the sentence. Thus, in part, a sentence can be looked upon as pairing these two subsets of states, i.e., as pairing a logical form with a pronounciation-determining structure. The Sponsor relation, which is a unique element of APG, exists largely to permit each state of the logical structure to be connected in a chain to one or zero states in the phonetically relevant structure. One would (correctly) expect no Sponsor relation in systems, like the artificial "languages" of logic, mathematics, and computer programming, in which the set of structures defining logical form is identical to the set defining the "realization" mode of sentences. The function of the Erase relation is to pick out from the set of all states in a sentence that subset which defines the superficial or phonologi­ cally relevant subpart. The set of states which are in the range of the Erase relation are not part of the subpart in question. In particular, any state which has a successor or replacer state is in the range of Erase and thus plays no direct role in phonological determination. Thus, a more accurate, informal structure for (1) would be (2) with the pairs Erase ((S3), (Si)) and Erase ((S4), (S2)). And a more accurate structure for (3) would be (4) with the pair Erase ((S5), (S2)) added. Diagrammatically: (5)

(S3)

(Si)

subject at l_2 of

direct object at L| of Clause;

(S2)

chSmeur at l_2 of

Naomi

(was)

jostl

(S2)

subject at L| of

(S5)

predicate at L| of

(S6)

predicate at l_2 of

14

1. INTRODUCTION

(6)

(S4) subject at L2 of

(Si) subject at L| of

Max

(S2) direct object at Li of :

Clausey

(S5) dm himself

(S3) pr« knows

(S6) predicate at Lg of

Of course, none of this informal description of sentence structure is or can be too clear. It will become such by considering the formal account which underlies it, in which all of the ideas here discussed are given pre­ cise formal reconstructions in terms of a few primitives of logically stan­ dard types, and in which the discussion can be formulated in terms of precise laws hypothesized to govern the class of objects which can be well-formed PNs in any human language. Our intention is to construct a formal theory of the domain of sentences looked upon in this way, i.e., where PNs, rules, and grammars are formally defined syntactic objects (in the logician's sense). Thus, formal APG grammars will be taken to specify infinite sets of formal objects called PNs. Each PN (well-formed for language L a ) viewed as a purely formal object has an interpretation, namely, that it describes some sentence in L a . We ate thus making explicit here, in a way not common in linguistics, that there are always two levels of discourse to be distinguished in theory construction, a purely formal or syntactic level in which one deals with formal objects without interpretation and the semantic level at which the objects of the syntactic level are assigned a (partial) interpretation. When

1.2. INFORMAL VIEW OF SENTENCES

15

we speak of sentences, grammatical relations, linguistic elements, etc., we are dealing with the semantic level, the level of interpreted objects. When we speak of PNs, L-graphs, etc., we are dealing with the purely formal level. Ultimately, in a field like linguistics, one constructs a formalism because one wants to make statements at the level of interpretation, i.e., statements about sentences, rules, grammars, etc. Therefore, one must attempt to construct a formal system which mirrors the presumed proper­ ties of the domain under study, the domain about which the formal con­ structs will be interpreted as making statements. Since we believe language involves linguistic elements, grammatical relations, sentences, rules, grammars, etc., our formalism will have to contain elements corre­ sponding to these. We begin the formal development of APG in Chapter 2. 1.3. Recent historical antecedents of APG About 1972, a number of linguists then working in the framework of TG (notably B. Comrie, E. L. Keenan, J. L. Morgan, D. M. Perlmutter, P. M. Postal, and J. R. Ross) recognized that grammatical relations such as subject, direct object, and indirect object play a central role in the syn­ tax of natural language. These authors came to the conclusion that these notions are needed in grammatical descriptions and theory in ways not anticipated or countenanced by standard TG. One line of development re­ sulting from this recognition was an unformalized model which retained transformations but took them as sensitive to grammatical relations. This was the approach of Keenan and Comrie (1972, published as Keenan and Comrie [1977]), who argued for a universal hierarchy of accessibility to extraction transformations based on grammatical relations. In a similar vein, Keenan (1976) attempted to define grammatical relations such as sub­ ject in terms of crosslinguistic uniformities in the behavior of subjects with respect to, among other things, transformations 9 (for a criticism of 9

Keenan s work is thus inconsistent with the basic RG and APG assumption that relations like subject are primitive.

16

1. INTRODUCTION

this attempt, see Johnson [1977b]). In another line of development that brought grammatical relations into prominence within a basically transfor­ mational model, Ross (1974), argued that a hierarchy of grammatical rela­ tions controlled the application of rules to constituents. In 1973, Perlmutter and Postal began to argue for the necessity of de­ veloping a theory of relational grammar (RG) based on the idea of taking the grammatical relations subject, direct object, etc. as primitives. This idea conflicted with central assumptions of TG, whose only relevant primi­ tives are linear order, labeling, and constituency, and which assumes (without argument) that relevant grammatical relations can be defined in a universally adequate way. 10 A number of concepts central to RG were de­ veloped by Perlmutter and Postal at this time, including the notions chomeur and term, and the idea of dispensing with transformations entirely for the statement of at least an important class of grammatical rules. It was proposed that these be formulated directly in terms of grammatical re­ lations like subject (e.g., Passive would be formulated as a rule which permitted a direct object to also be a subject). This period saw the de­ velopment of a number of hypothesized universal laws of grammar by Perlmutter and Postal, including those named The Relational Succession Law, The Relational Annihilation Law, The Host Limitation Law, The Motivated Chomage Law, The Cyclicity Law, The Reranking Law, The Advancee Tenure Law, The Reflexivization Law, The Coreferential Dele­ tion Law, and The Agreement Law (Perlmutter and Postal [1974] and Postal [1974b]). The same period saw the development of The Continuous Segment Principle by Johnson (1974b, 1977a). 10 Attempts within TG to define grammatical relations have remained curious­ ly insensitive to the empirical difficulties. Almost a quarter of a century after the initial proposal (Chomsky [1955:254]) that the subject and direct object rela­ tions could be defined in terms of the bracketings provided by NP+ VP analyses of clause structure, we know of no published discussion of the immediate diffi­ culties (see Johnson [l974b, Chapter 2]) raised by, inter alia, the unquestioned existence of languages with VSO clause structures, languages in no way lacking subject and direct object relations (see Bell [ΐ97δ] for discussion of this point with respect to the VSO language Cebuano, and Anderson and Chung [l977] for more general remarks).

1.3. RECENT ANTECEDENTS OF APG

17

Within the history of RG, the years between 1972 and 1975 mark a period we can refer to as stage 1 RG. This is characterized by the view, taken, of course, from TG work, that sentence structure is properly representable by a sequence of structures (a derivation). This view differed from TG accounts in assuming that at least a subset of the structures in a derivation would not be phrase markers in the TG sense, but rather depen­ dency trees with branches labeled with the names of grammatical relations. No formal theory of RG was developed to represent these ideas, however. The period beginning in 1975 we refer to as stage 2 RG. It is charac­ terized by the view that sentence structure is properly characterized in terms of a single graph-theoretic object called a Relational Network (RN). 11 The formulations corresponding to this stage have sometimes been referred to as "uninetwork RG." The basic idea of eliminating derivations in favor of a single network structure came from two independent sources. The first was a proposal of W. Rounds made at the SSRB seminar on Formal Models in Linguistics held in association with the 1974 LSA Lin­ guistic Institute at Amherst, Massachusetts in August of that year. The other was a series of proposals made by G. Lakoff in unpublished work in the fall of 1975 (see Lakoff [1977] for a development of some of these ideas). 12 At this point, Perlmutter and Postal introduced the partially formalized notion ^rc as an explication of the notion of a grammatical re­ lation holding between two entities at a given linguistic level, and the partially formalized notion Stratum as a reconstruction of the notion of linguistic level. RNs were considered to be simply sets of arcs (see Postal [1977], Perlmutter and Postal [1977], to appear a). While these were important steps in the development of a formal theory of relational

This term was apparently first used in Johnson (1974b), to refer essential­ ly to dependency trees with branches labeled with the names of grammatical relations. 12 Independently, Hudson (1976) has presented a similar idea within his theory of daughter dependency grammar.

18

1. INTRODUCTION

notions, RG at this stage nonetheless remained an essentially unformal­ ized set of ideas. During this period, Perlmutter and Postal made a number of changes in the system of proposed universal laws, abandoning some (e.g., The Reranking Law), modifying others, and proposing some new ones. Much additional empirical research in the framework was carried out during this time, not only by these researchers, but also by D. E. Johnson (see John­ son [1977a, 1977b, to appear]), by many students of Perlmutter, and by others. For an overview of the work of Perlmutter and Postal during this period, see Perlmutter (to appear a, to appear b). The origin of APG dates to February 1977. It was born accidentally, arising from an attempt to construct a formal linguistic theory underlying the basic ideas of RG. APG accepts as correct the basic RG insight that primitive relations like subject, chomeur, etc., are fundamental to the characterization of linguistic structure. It incorporates and formalizes the fundamental RG notions of Arc (see Chapter 2) and Stratum (see Chapter 6). However, in the course of formalizing these RG concepts it became neces­ sary to incorporate into APG two new, more basic concepts—the primitive, binary relations between arcs, Sponsor and Erase. While the APG notion R-graph (see Chapter 2) corresponds in essence to the informal RG notion RN, APG R-graphs are only a derivative aspect of PNs, defined in terms of the more basic notions. RG claimed that sen­ tence structure was representable as a whole in terms of RNs. APG claims that R-graphs are only a subpart of overall sentence structure represented by PNs. One consequence of the failure of RG to recognize the relations Sponsor and Erase, and its effective limitation of attention to R-graph aspects of structure, is that no notion of Successor or Replace was possible (see Chapter 5, and passim). RG did not recognize that there are relations between arcs and thus, from an APG viewpoint, missed the central aspect of linguistic structure. It will be seen that relations between arcs, both the primitive relations Sponsor and Erase, and the many derived relations defined in terms of these, are central to the statement of

1.3. RECENT ANTECEDENTS OF APG

19

almost all APG PN laws and language-particular rules. The extra dimen­ sion of linguistic structure formalized in terms of Sponsor and Erase is thus the essential feature that distinguishes the APG conception of human sentence structure from other conceptions. This radically different view of sentence structure permits, significantly, a correspondingly novel con­ ception of grammatical rule (see Chapter 14). Naturally, the formalization of RG notions in APG terms has raised a number of questions that could not arise in (i) an informal framework, and (ii) a framework not involving Sponsor and Erase. These questions have led to the formulation of a host of new hypothesized laws of grammar. Thus, while the present APG work incorporates formalized accounts of a few previous RG laws, most of the PN laws proposed in the present work have no RG antecedents. While the preceding sketch has traced the development of some theo­ retical notions incorporated into a formal theory in the present work, little mention has been made of the empirical studies carried out in the RG framework. However, these studies provide considerable justification for the theoretical notions at issue, and they have served to define the empiri­ cal constraints which we assume a theory of grammar must meet. A de­ tailed consideration of these studies and their important implications unfortunately lies beyond the scope of the present work.13 1.4. Intermezzo on linguistic theory Before continuing, it is important to sketch very briefly our conception of APG linguistic theory. This will contain, in addition to whatever de­ vices from logic are necessary (see section 1.5), the following items:

13 A by no means complete list of relevant works includes Aissen and Perlmutter (1976), Bell (1974, 1976), Chung (1976a), Frantz (1976), Harris (1976, 1977), Jacobson (1975), Johnson (1974a, 1974b, 1977a, 1977b, to appear), Lawler (1977), Morgan, Green and Cole (1976), Perlmutter (1978, to appear a, to appear b), Perlmutter and Postal (1977), and Pullum (1977).

20

1. INTRODUCTION

(7) a.

A set of specified primitive linguistic terms.14

b. A set of definitions, specifying a set of defined constructs in terms of primitive elements, other defined constructs, and logical devices. c. A set of grammatical laws. d. A set of theorems.15 As (7a, b) are relatively straightforward, we concentrate on (7c, d). Be­ cause of the character of grammatical study, the linguist is concerned with four separable kinds of entity, sentences, collections of sentences (call them corpora for convenience), rules, and collections of rules (called grammars). It is the job of linguistic theory to characterize possible sen­ tence, possible corpus, possible rule, and possible grammar. Internal to APG linguistic theory, sentences are reconstructed in terms of PNs and the task in question is then equivalent to characterizing the class of possible PNs. Analogously, there are the tasks of characterizing internal to APG theory possible corpus, possible linguistic rule, and possible grammar. It is thus convenient to distinguish terminologically four types of laws, imposing universal conditions on respectively possible PNs,

14 In certain cases, what is involved is particular sets, e.g., the set of gram­ matical category nodes, whose members are interpreted as representing internal to the formalism the class of possible grammatical categories. In general, we are not in a position to specify the membership of such sets completely at this point, linguistics being an empirical field in an early stage of development. However, no issue of real theoretical relevance is raised by this inability. ^Theorems are, from a purely logical point of view, redundant. From an abstract viewpoint, a theory specified only in terms of (7a,b,c) makes the same claims about a given subject matter as does one with (7d) included. However, it is in general not obvious what the implications of a given theory sans theorems are. Thus, in practice, theorems are, in the case of a theory of any complexity, quite essential to determining what the theory "says" about the subject matter under study. Since the present theory involves hundreds of laws and definitions, the question of ultimate implications of the combination of these arises very strongly. Theorems are then central to the task of determining the adequacy of a given empirical theory of this type: empirically supported theorems support the general theory, empirically discontinued ones serve to undermine it.

1.4. INTERMEZZO ON LINGUISTIC THEORY

21

corpora, rules, and grammars. One can refer to these as PN laws, Corpus Laws, Rule Laws, and Grammar Laws. From these laws (and the defini­ tions) various theorems follow. These, while adding no new content to the theory from the logical point of view, prove that the objects under study (in this case, PNs, corpora, rules or grammars) have properties which may not be obvious from the statement of the laws themselves. For various reasons, we are in a position to propose a rather large set of PN laws but hardly any Corpus laws, Rule laws, or Grammar laws. In­ deed, for reasons touched on in Chapter 14, in the current framework it is even possible to doubt that there are rich sets of rule and grammar laws. Two grammar laws which most linguists would in effect assent to are: (8) a. Potential Grammar Law 1 (VX) (Grammar (X) -> Finite (X)) b. Potential Grammar Law 2 (VX) (Grammar (X)

Not (X= 0)) .

Given that a grammar is a set of rules, (8a) says that such sets have finite bounds, while (8b) says that such sets cannot be empty. However, while (8a, b) are, we are confident, true of the grammars of all attested languages, we deny that they are proper elements of grammatical theory. For everything they could account for is an independent consequence of other true assumptions about human beings. Space precludes a discussion of these topics here (see Postal [to appear a]). The laws and theorems of APG linguistic theory make (indirectly) em­ pirical predictions about the class of objects that can be found in natural languages. PN laws and theorems exclude as impossible for any human language vast numbers of a priori possible PNs, and the claim that sen­ tences are PNs excludes all those objects which are not PNs. Rule laws limit the class of possible rules, ultimately, to just those which can be instantiated in some possible language. And Grammar laws limit the classes of (Rule law-permitted) rules which can combine to form legal grammars.

22

1. INTRODUCTION

A formalization in these terms will thus involve a specification of those primitive linguistic terms necessary to formalize PNs, rules, and grammars, definitions of defined concepts relevant for these three, and statement of the four types of law. This work deals almost exclusively with PN laws and theorems derivable from these. In this volume, we formally state and discuss 116 PN laws and prove 134 theorems, providing an initial hypothesis strongly restricting the notion of well-formed PN for any language. A final word is in order about the material that follows. There are two distinguishable aspects of any reasonably developed system of linguistic ideas. Such a system forms first what can be called a theoretical frame­ work. A framework is a set of interrelated concepts and assumptions which defines a general approach to the description of the subject matter and which involves a basic view of the nature of the objects to be charac­ terized. The APG framework is defined by (i) the view that sentences are properly reconstructed as PNs, (ii) the view that all grammatical rules are material implications, (iii) the view that well-formedness is characterizable in terms of model-theoretic satisfaction, and (iv) all the concepts which (i) through (iii) presuppose. Among the latter are, most crucially, the set of primitives underlying PNs. A theory is much more restricted and difficult to achieve. It is ob­ tained by building from the elements of a framework a rich set of laws which, by generating appropriate theorems, make empirical predictions about the subject matter. In the present case, APG theory so far consists of the 116 PN laws proposed, together with the theorems proved on their basis, along with all of the defined concepts necessary for the statement of these laws and theorems. It also consists of the partial formalization of rules and well-formedness given. While there is some limited sense in which frameworks may be true or false (i.e., it either is or is not the case that PNs reconstruct sentences properly), it is, in general practice, not really feasible to empirically con­ firm or disconfirm frameworks, because of their vagueness, imprecision,

1.4. INTERMEZZO ON LINGUISTIC THEORY

23

degree of abstractness, and lack of specificity. Therefore, normally, frameworks are eliminated only when a better framework (one perceived as better) replaces it. Hence, it is possible and normal to have much greater confidence in the correctness of a framework than in a particular theory based on it. Once a framework is established, it is common for its basic assumptions to remain unquestioned, at least by those who accept the framework. These assumptions simply come to define the basis of inquiry. A corollary of this is that many aspects of a theory can be wrong without undermining, either intellectually or socially, the framework which under­ lies that theory. In the present work, we have tried to do two things. First, we have developed and presented an extensive new framework. But, second, and rather unusually (and perhaps a little rashly), we have gone beyond this and developed, within the terms of this new framework, an extensive, ex­ plicit linguistic theory, composed largely of the PN laws and those theo­ rems we have been able to prove. While we have made every effort to propose reasonable and apparently valid PN laws, it would not be surpris­ ing if many of these proved incorrect or in need of some modification or restriction. This would mean, literally, that the theory as presented here is not entirely correct. But this would not necessarily have negative im­ plications for the framework, which is, of course, compatible with an enormous range of possible distinct theories. An analogue with TG might help. The incorrectness of, e.g., The Coordinate Structure Constraint pro­ posed by Ross (1967a) (an analogue of one of our PN laws) would not serve to undermine the entire TG framework, nor would the incorrectness of many other TG assumptions, again largely because frameworks are for the most part too vague to really be disconfirmed. In other words, our strongest belief, naturally, is in the correctness of the APG framework, presupposed by the theory. The proposed PN laws are independent of the framework in the sense that each could be incorrect without showing the framework was incorrect. However, the incorrectness of all of them would cast some doubt on the possibility of constructing a

1. INTRODUCTION

24

valid theory on the basis of the APG framework. Here also though, one can draw distinctions. There is a range of more central, core PN laws which plays a much greater role than others, and whose abandonment would have far greater consequences. Thus, from another point of view, it is possible to regard a certain subset of more basic PN laws more as part of the APG framework than as part of a particular theory. 16 In con­ trast to various highly particular PN laws which involve quite specific assumptions about particular construction types or particular grammatical relations, the following very general and fundamental PN laws play a role almost everywhere. PN law 1. The Replacer Erase Law PN law

2. The Successor Erase Law

PN law 3. The Unique Eraser Law PN law 4. The Self-Sponsor Law PN law 5. The Local Successor Distinct R-sign Law PN law 6. The Sponsor Independence Law PN law 7. The Maximal Two Sponsor Law PN law 12. The Immigrant Local Sponsor Law PN law 13. The Graft Overlap Law PN law 21. The No Vacuous Fall-Through Law PN law 26. The Fall-Through Law The other coordinate laws of Chapter 6 PN law 94. The Internal Survivor Law PN law 107. The Closure Law Although we regard these as ultimately testable empirical claims, and thus methodologically on a par with other more specific and less "deep" laws, they play such a basic role in defining the APG approach to lan­ guage that they certainly deserve to be highlighted. One way in which

^Our hesitancy here is a reflection of the fact that the line between frame­ work and theory is vague.

1.4. INTERMEZZO ON LINGUISTIC THEORY

25

the centrality of these principles is most evidently manifested is their role in the proofs of theorems. Few of the theorems in the present volume could survive the elimination of these laws. These principles would thus either cease to be theorems, or would require new proofs independent of the laws in question.

1.5. Notation and technical symbols As in any intellectual work, we necessarily make use of concepts from logic and mathematics: propositions, negation, sets, quantifiers, predi­ cates, variables, numbers, etc. We allow ourselves this apparatus freely without special note. We here bring together a number of the more particu­ lar and technical devices drawn from logic and mathematics with English equivalents for technical symbols and a few notes. (9) Logico-Mathematical Devices Concept/Symbol

Explication

a. Finite b. Sequence c. Ancestral

See Quine (1958: 250-253) (Xj'--X n ) "X 1 --X n is a sequence of elements" A relation defined in terms of a given relation R, i.e., the ancestral of R . Informally, to paraphrase Quine (1958: 216), the ancestral of R is the rela­ tion of X to Y such that X is Y or else bears R to something which bears R to Y , or else, etc. For a rigorous formulation, see Quine (1958: 216), Carnap (1958: 147). Note that, regardless of the reflexivity of R, the ancestral of R is a re­ flexive relation. An ordered pair of the elements Χ, Υ. (X, Y) (Υ, X) The universal quantifier, "for all···." That is, (VX)(F(X)) = "for all X, F(X)." The existential quantifier, "there exists a." That is, (3X)(F(X)) = "there exists an X, F(X)" The predicate of set membership. That is, XfY = "the element X is a member of the set Y." Negation of (i) These enclose representations of sets The null set, i.e., the set with no members Set inclusion. That is, XCY = "X is included in Y." Identity Nonidentity Material implication. That is, P->Q = "if P then Q, i.e., not (P and not Q)." Biconditional. That is, PQ is equivalent to P-»Q Λ Q->P = "P if and only if Q."

d. (X,Y) e. V

f. a g· (i)

e

(ϋ) ί h. S ! i. Φ j· C k. (i) = (ϋ) ^ 1 . (i) (ii)

26

1. INTRODUCTION

Concept/Symbol

Explication

m. (i)

And Or Negation Less than Less than or equal to Greater than Greater than or equal to Not greater than Cartesian Product of X and Y. That is, the set of all ordered pairs such that the first member of a pair (X and the second member of a pair fY . The concatenation operator, an operator on strings of symbols. For an axiom system for this, see Rosenbloom (1950: 189).

A

(ii) V

n. Not o. (i)


(iv) >

(v) > p.

XxY

q. +

In addition, by general convention, where "-" or

is the main

connective of a formal statement, the antecedent and consequent expres­ sions are not flanked by parentheses, e.g.:

(10)

" X - Y a Z " abbreviates "(X ) - ( Y a Z ) " " X v Y - Y v ( X a Z )" abbreviates " ( X v Y ) - ( Y a ( X v Z ) ) " . A major simplifying convention used throughout this work is:

(11) Universal Quantifier Scope Suppression Convention In a given formal statement (PN law, definition, theorem, rule), uni­ versal quantifiers with "widest scope," i.e., which have the entire statement except other universal quantifiers in their scope, are suppressed. For example, given convention (11), (8a) above would be written simply as (12) = (8a) Grammar (X) - Finite (X) . To take another example, PN law 3, The Unique Eraser Law, is given in (13) with convention (11) and in (14) without it (see (5.19)): (13) PN Law 3 (The Unique Eraser Law) Erase (A, B) A Erase (C, B) - A=C

1.5. NOTATION AND TECHNICAL SYMBOLS

27

(14) (VA)(VB)(VC)(Erase(A, B) A Erase(C,B) -* A = C) . Without convention (10), (14) would be:

Furthermore, instead of explicitly restricting variables in each case to an appropriate domain (e.g., the variables A, B, and C in (13)-(15) appropriately range over the set of arcs), we make use of the following set of general conventions for variables, summarized in tabular form: (16) Table of Variables a. Restricted Variables 1. Nodes 2. R-signs 3. Arcs 4. Coordinates 5. Coordinate Sequences 6. L-graphs 7. R-graphs 8. S-graphs 9. PPNs 10. PNs b. Unrestricted Variables Without any of the above conventions, a relatively simple PN law like (13) above would look like:

Finally, we institute the following convention, analogous to conjunction reduction in natural language:

28

(18)

1. INTRODUCTION

Subparts of statement of the form:

for an arbitrary, unary predicate,

Pred, are abbreviated respectively as:

For example, (20) would be written as (21):

T h e s e conventions are used merely to- make the formal statements of this work easier to read.

They have no theoretical import.

CHAPTER 2 GRAPH-THEORETIC ASPECTS OF APG 2.1. Primitives and basic defined sets As indicated in Chapter 1, in the APG framework, sentences are re­ constructed in terms of formal objects referred to as PNs. In the present chapter, we introduce and develop those formal features of PNs which are, in effect, naturally describable in terms of objects studied in the branch of mathematics called graph theory. We begin by considering the primitive elements of the theory. PNs are formal objects which involve seven types of primitive: (1) The Primitive Constructs Underlying PNs a. A denumerably infinite set, NTNo , of elements called nontermi­ nal nodes. b. A (finite) set, LNo , of elements called logical nodes. c. A set, PNo , of elements called phonological nodes. d. A finite set, GNo , of elements called grammatical category nodes. e. A finite, and relatively small (say less than one hundred) set, REL S, of relational signs (R-signs). f. Averysmallfiniteset Se lj C 2j --^c n I of numbers called coordinates. g. Two primitive relations (between arcs, see below) called Sponsor and Erase. Because Sponsor and Erase go beyond graph-theoretic considerations, they will not be discussed until a following chapter. Under the intended interpretation of PNs as representing sentences (but see note 1 of Chapter 1), R-signs are the names of the primitive

30

2. GRAPH-THEORETIC ASPECTS OF APG

grammatical relations taken to occur in the sentences of human languages, that is, the names of members of PGR . The members of REL S thus represent the undefined grammatical relations taken to hold between primi­

tive lingpistic elements. The latter are represented in the formalism of PNs by the various types of nodes indicated in (la-d). Our assumption is that the members of PGR are all binary, irreflexive, asymmetrical relations. 1 These properties of the relations will, as seen

below, naturally lead to the imposition of corresponding formal conditions on what a possible PN can be. Among the relations assumed to be mem­ bers of PGR are those in (2) below, with the corresponding R-signs in­ cluded in Rel S given in parentheses. Note that we do not here follow strict logical usage in that, in many cases, the same inscription is used for a relation and for its name (R-sign), i.e., we suppress quotes for names. This should cause no confusion since the entire formal development of PNs involves R-signs, members of Rel S. Reference to members of PGR is relevant only when considering the interpretation of the formalism. (2) A Few Relations f PGR and Their Names (in parentheses) ( Rel S. Linear Precedence (LP)

Indirect Object or 3 (3)

Labels (L)

Chomeur (Cho)

Conjunct (Con)

Union (U)

Marquee (Marq)

Dead (Dead)

Flag (F)

Instrumental (Inst)

Restrictive Relative (RR)

Locative (Loc)

Predicate (P)

Benefactive (Ben)

Subject or 1 (1)

Genitive (Gen)

Direct Object or 2(2)

^In general, the members of PGR are not transitive, in fact, they are in­ transitive. One partial exception is the relation of linear precedence, which is generally transitive. For some discussion of this relation, more precisely, its correspondents internal to the formalism, see Chapter 12.

2.1. PRIMITIVES AND BASIC DEFINED SETS

31

Consider the various types of node in (la-d). Nonterminal nodes are intended to represent abstract linguistic entities like clauses, phrases, etc. They have no inherent "substance" or distinguishing features be­ yond their distinctness from each other. They are, in this respect, analo­ gous to the variables of a logical system. Nonterminal nodes can, there­ fore, naturally be identified with positive integers, as in Lakoff's (1970) conception of correspondence grammar. However, we use the integers 1, 2, and 3 as names for certain grammatical relations, and they are thus in­ cluded in the set Rel S, which must be disjoint from NTNo . Therefore, we specify that the first integer in NTNo is 4. (3) NTNo = !4,5,6,···! . The set LNo is intended to contain all and only those primitive ele­ ments needed for logical or semantic description, excluding names, see Chapter 4. Thus, in this class might be a node representing a logical atomic predicate LOVE,2 a node representing an operator like the univer­ sal quantifier, etc. We will not attempt to consider the membership of this set in detail. However, LNo will not contain any elements corre­ sponding to the constants or variables of logical description. These are naturally represented in our terms by elements of NTNo . The members of GNo will include no doubt such elements as Cl(ause), Nom(inal), Masculine (for languages like Spanish and Chinook with nonsemantic gender), Prep(osition),3 etc. We discuss certain mem­ bers of GNo in greater detail in Chapter 7. There is no need to recog­ nize a member of GNo like the node Silent of Postal (1977). This element was proposed in a pre-APG relational framework as a device for

2

We systematically represent logical nodes with the capitalized versions of English word spellings, phonological nodes with ordinary spellings. 3 Actually, since the difference between prepositions and postpositions is purely one of linear ordering, there should be at worst a single category covering both.

32

2. GRAPH-THEORETIC ASPECTS OF APG

indicating the nonappearance of certain kinds of elements in "surface" forms. However, in the present framework, a much more elegant and gen­ eral mechanism is proposed, utilizing one of the most basic APG concepts, namely, the Erase relation. This mechanism accomplishes the task attrib­ uted to the now unneeded node Silent (see the discussions of self-erasing arcs in Chapters 3 and 9). The members of PNo are, in the current version of APG, intended to represent particular (morpho)phonemic forms of morphemes. For example, there would be a phonological node /pi/, "pea". We thus take phonologi­ cal nodes at this stage to be grammatical atoms, although from the point of view of phonology they are, of course, molecular, i.e., they have an in­ ternal structure. This assumption is an artifact of a practical decision to ignore phonology for the moment. Ultimately, we are confident that an APG approach to phonology is possible. In such a version, phonological nodes would no doubt correspond to individual phonological features (see Chapter 12, section 8). LNo , PNo , and GNo are disjoint primitive sets. A basic initial assumption of APG, however, is that their union forms an important theo­ retical class, the class of terminal nodes, which jointly contrast with the nonterminal nodes in NTNo :

(4) Def. 1: a e TNo ^ a e LNo ν a e PNo ν a e GNo . Moreover, the classes of terminal nodes and nonterminal nodes together form an important class, the class of nodes: (5) Def. 2: a e No , n>0, be a finite sequence of η 1 η coordinates. Then: CoordinateSequence () (Vj, 1 < j < η - l)(ij +1 = ij +1) .

2.2. Three notions of "Arc" Our medium-range goal is to give a formal definition of the notion PN. A closer goal is to define the concept Relational Graph (R-graph). To do

34

2. GRAPH-THEORETIC ASPECTS OF APG

this, we first need three subsidiary concepts successively definable in terms of the primitives and defined notions of 2.1: (7) a. primitive arc b. incomplete arc c. arc A Primitive Arc is simply an ordered pair of nodes from No . (8) Def. 4: Primitive Arc (X t V) «-> X e No

Λ

Y e No .

Thus, given two nodes, a, b, there are a priori two possible primitive arcs, which we will write equivalently as in: (9) Notation for Primitive Arcs (a, b) = a

J

b

^

b

I

a

What we are here calling "primitive arcs" correspond most closely to what are normally referred to in graph-theoretic discussions simply as "arcs," "directed lines," "otiented lines," etc. But our conception of primitive arc differs formally from the standard graph-theoretic notion of a directed line in the following respects. In graph theory, lines (or arcs) are taken as primitive along with a set of elements called points or verti­ ces (essentially, our nodes). The direction of each line, i.e., roughly the contrast between the two arrows in (9), is characterized by two primitive functions, f and s, f identifying the "first" node, s the "second" node (see Harary, Norman, and Cartwright [1965: 4, 5]). Since this approach would increase the number of APG primitives with no apparent linguistic gain, we have opted to depart from standard graph theory by not postulat­ ing a primitive set of lines and the functions f and s . However, it should be clear that the current approach can be given a standard graphtheoretic interpretation in a straightforward fashion.

2.2. THREE NOTIONS OF "ARC"

35

Terminologically, we have not used the simpler term "arc" for what we call "primitive arc" because primitive arcs as such play almost no role in out ultimate constructions. They figure as building blocks. There­ fore, we reserve the simpler term "arc" for elements of a type which actu­ ally have direct linguistic significance, and which are thus constantly referred to. The members of an ordered pair of nodes are referred to as first and second nodes. First nodes are, in accord with standard mathematical practice (see Harary, Norman, and Cartwright [1965: 4]), written at the arrow tails in the arrow notation of (9). Second nodes are thus written at the arrow heads. We also refer to the first node in a primitive arc as the tail or governor node, the second node as the head or dependent node. It is convenient from many points of view to talk about primitive arcs by using relational notation. Informally, if (a, b) is a primitive arc, we say that a bears the Govern relation to

b, i.e., Govern (a, b). Actually,

we later define "Govern" in terms of arcs rather than primitive arcs, so the current discussion is slightly illegitimate. Conversely, if Govern (a, b), we say Depend (b, a) . Moreover, it is useful on many occasions, and cru­ cial on others, to introduce the ancestrals of these two relations, R(emote)Govern and R(emote)-Depend. 4 Thus, given primitive arcs (a, b), (b, c) and (c, d), R-Govern (a, b), R-Govern (a, c), R-Govern (a, d), R-Govern(b, c) , R-Govern (b, d) , R-Govern (c, d) , R-Govern (a, a) , etc. We see later that, ignoring primitive arcs associated with R-signs LP and L , our notion Govern corresponds fairly closely to the transformational/ structural notion of the immediate constituent relation, while R-govern corresponds to the more general constituency relation. A propos of Govern and R-govern, it is important to freely allow, henceforth without explicit note, the ancestrals of all the primitive and

4 Our notion R-depend is equivalent to the concept Reachable of Harary, Norman, and Cartwright (1965: 32).

36

2. GRAPH THEORETIC ASPECTS OF APG

defined relations in APG. Moreover, we systematically denote these as follows: (10) Notation Given APG relation = R Ancestral of R = Remote-R = R-R . An Incomplete Arc is a pairing of one primitive arc with exactly one member of Rel S. That is, each incomplete arc is a set whose members are one primitive arc and one R-sign: (11) Def. 5: Incomplete Arc (X) *-* (3W)(3Z)(X = i W, Z\ a W f Rel S a Primitive Arc(Z)) . Suppose GR x is some member of Rel S. Then we represent the associa­ tion of GR x with primitive arc (a, b) equivalently as in: (12) Notation for Incomplete Arcs a GR x (a, b) = GR x b APG linguistic theory thus makes available a priori a denumerably infin­ ite set of incomplete arcs, namely, that set formed by combining any primitive arc with some R-sign. There are an infinite number of primitive arcs because there are an infinite number of nonterminal nodes. However, the set of incomplete arcs is restricted to a finite number of types, each type defined by a single R-sign. Later chapters establish various typolo­ gies of arcs which depend on these incomplete arc types. An arc in our sense is a pairing of an incomplete arc with a nonnull coordinate sequence: (13) Def. 6: Arc(X) «- (3W)(3Z)(X = iW, ZI Λ Incomplete Arc(W ) A Coordinate Sequence(Z)) .

2.2. THREE NOTIONS OF "ARC'

37

The arc determined by associating with the incomplete arc GR x (a, b) the coordinate sequence will be written equivalently as either: (14) Notation for Arcs

[GR1Xaf b)< α >] = GR v

Recall that our convention is to represent nodes by early small letters, sometimes subscripted numerically, and to represent coordinates with the small letter c subscripted numerically. Variables over coordinate sequences are, recall, represented as Greek letters. Arcs in the sense just defined are the real building blocks of PNs, or, more precisely, of R-graphs, which are components of PNs. Thus, arcs are the elements having real linguistic significance. Informally, an arc is the formal representation of what was in Chapter 1 called a linguistic state: an arc represents the existence of a relation at a nonnull sequence of levels. It is this centrality of arcs which leads us to reserve the sim­ plest term for them, relegating the terms "primitive arc" and "incomplete arc" to simpler concepts, even at the cost of deviating from what might be expected from familiarity with relatively standard graph-theoretic usage. 2.3. Interpretation of incomplete arcs and arcs We are moving toward defining the notion R-graph, which will be a set of arcs meeting certain conditions. Before getting to this, we clarify briefly the intended linguistic interpretation of the formal objects called incomplete arcs and arcs. Under the intended interpretation of PNs as reconstructing sentences, R-graphs, in effect, represent all structure except that involving Sponsor and Erase. Consequently, R-graphs represent sets of grammatical rela­ tions holding between elements, these stratified into linguistic states.

38

2. GRAPH-THEORETIC ASPECTS OF APG

Each arc in an R-graph represents a continuous sequence of one or more linguistic states, the coordinates of the arc representing the levels, the incomplete arc representing the relation (extensionally, the membership of the ordered pair of elements in the primitive arc of the incomplete arc in the set of such pairs which is the relation). We can make the interpretation discussion more formal if we introduce the following notation. Let nodes a, b,

c

represent respectively the lin­

guistic elements a, b, c; let R-sign GR x be the name of PGR member GR x ; let Q be the sentence (partially) represented by R-graph Q and

let α be the sequence of levels represented by coordinate sequence . Finally, let R (w, v) mean that the pair (w, v) is in the relation R , for arbitrary R e PGR . Then, the principle of interpretation for incomplete arcs can be given more precisely as: (15) The Principle of Interpretation of Incomplete Arcs For all R-graphs Q , 5 GR x (a,b) is an incomplete arc in Q 6 if and only if a, b are in Q and GR x (a, b). And, extending the description to arcs, we can say: (16) The Principle of Interpretation of Arcs Forall R-graphs Q, [GR x (a,b)] is an arc in Q if and only if a,b,a are in Q and, for all levels L in the sequence β in Q , GR x (a, b) holds at L . (15) and (16) express how incomplete arcs and arcs (which, as such, are pieces of uninterpreted formalism, involving nodes, R-signs, and coordinate sequences) are related to the presumed real elements of human

Since we have not formally defined "R-graph," this is not really legitimate. However, for purposes of understanding (15), the reader may identify an R-graph with any finite, nonnull set of arcs. ^The reader might compare this principle of interpretation with an analogous statement in Harary, Norman, and Cartwright (1965: 363).

2.3. INCOMPLETE ARCS AND ARCS

39

sentences. Thus (15) and (16) are not principles internal to APG linguis­ tic theory viewed as a formal system, but semantical principles which indicate how the formalism of PNs (partly) relates to the objects about which APG theory makes claims. Informally, one can paraphrase (15) as saying simply that incomplete arcs represent the fact that grammatical re­ lations hold between specified pairs of linguistic elements, while (16) says that such pairs are in such relations only at fixed sequences of levels.

2.4. Properties of arcs and sets of arcs To facilitate the ultimate definition of "R-graph" and much later dis­ cussion, it is important to introduce concepts which permit effective de­ scription of various significant graph-theoretic properties of sets of arcs. Prior to that, it is useful to introduce the possibility of referring to arcs in various ways without having to specify their full structure. First, it is extremely useful to have terms which permit one to discuss the first or second nodes, or both, of an arc, without having to mention its R-sign, coordinates, or other node. We thus introduce the concepts Tail, Head, and Endpoint to permit this, as follows: (17) Def. 7: Tail(b,A) \ I — (3GR v )(3a)(3a)(A=[GR v (b,a)]) . Tail(A)= b) (18) Def. 8: Head (a, A) \ } — (3GR x )(3b)(3a)(A=[GR x (b,a)]) . Head(A) = a) (19) Def. 9: Endpoint (a, A) «-» Head (a, A) ν Tail (a, A) . (20) Def. 10: Endpoints (a, b, A) GR x arc (Α Λ B). (22) Def. 13: X arc (A) ~ GR y arc (A) Λ GR y e X . Definition 11 thus permits us to talk about LP arcs, 1 arcs, P arcs, etc., without having to specify anything about the nodes or coordinates of those arcs. Assume that there is a class of R-signs called Term = {1,2, 31. Definition 13 then permits reference to Term arcs, with no further specifi­ cation required, and similarly for any other defined sets of R-signs. Finally, it is in many cases desirable to refer to the coordinate sequence of an arc without having to worry about its R-sign or nodes. Therefore: (23) Def. 14: K a c 1 - ΰ η β > ( Α ) ^ (aGR x )(aa)(ab)(A = [GR x (a f b)] . Definition 14 permits one as it were, to "extract" the entire coordinate sequence from an arc. However, it is often only relevant to refer to a sub­ set of the coordinates, sometimes only one. Hence we allow ourselves the following abbreviatory convention: (24) Notation ck

1

-" c W ( A ) = η

] , a^b^c^d.

The relevant analogy here is between two different ways of representing two sets whose distinct elements are respectively a, b and b, c . On the one hand, one can represent them, in standard notation, as: (63) U,b|

ib,c}.

But one could also construct a notation which avoids repetition of shared members, say that yielding: (64) j ai b I c ! . 12 12 (64) bears the same kind of relation to (63) as (61) does to (60). The dif­ ference in both cases is notational, and hence substantively irrelevant. Therefore, one is free to pick the most useful notation for the purposes at hand. And, for representing linguistic structures on paper, the notation of (61) is superior to that of (60), a superiority which grows as the complexi­ ty of the structures to be represented grows. One further comment is in order. In adopting the notation of (61), we are led automatically not to repeat any nodes in R-graphs, terminal nodes included. Therefore, in representing a sentence like: (65) This man hates that man. there would be only one occurrence of the terminal node man, heading two distinct L arcs, e.g., an R-graph fragment like:

2.6. NOTATIONAL POINTS

59

This may seem strange at first. It runs counter to normal notational practice in transformational linguistics where, e.g., the symbol NP is written in representations as many times as there are nodes to be catego­ rized as members of the category NP. However, there are complex examples where the notation in (66) would lead to a maze of crossing lines, making comprehension difficult. In these cases, we write terminal nodes more than once in the representation of a single R-graph. We make an attempt to place the R-sign of an arc to the left of the line representing that arc, the coordinate sequence to the right. Usually this should cause no confusion but in some cases, e.g., (66), it leads to up/down reversals, i.e., R-signs occur both above and below their arcs. None of this is of any significance. Also irrelevant is the point on the arrow at which R-sign and coordinate sequence are affixed. All such matters are determined purely by clarity and convenience and have no lin­ guistic significance. Finally, our knowledge of linguistic structure is limited and fragmen­ tary. Hence we inevitably leave out much of the structure of any repre­ sented case, often without explicit comment. No conclusions should be drawn from this beyond the obvious one just stated. For example, the fact that we represent a particular sentence without logical nodes is not a claim that there are sentences without logical elements, etc.

CHAPTER 3 ARC PAIR RELATIONS 3.1. /nirociuciion ίο the Sponsor and Erase relations In this chapter, we informally discuss the primitive relations, Sponsor and Erase. This discussion will serve as an introduction to the more ex­ tensive, formal development of the central notion PN, which involves the formal correspondents of Sponsor and Erase. As mentioned in Chapter 1, Sponsor and Erase are both binary relations holding between (in some cases unary) sequences of linguistic states. The basic idea behind these two concepts can perhaps be best understood by way of illustration. Consider: (1) John was kissed by Lois. Under our informal conception, the structure of (1) involves, in part, two linguistic levels, say L^ and Lj. At level Lj, Lois bears the 1 rela­ tion, and John bears the 2 relation, to the clause. 1 At level Lj, it is John which bears the 1 relation, while Lois bears the chomeur relation, to the clause. Roughly: (2) L i : 1(55, Lois), 2 (55, John) Lj: chomeur(55, Lois), 1(55,John) (where 55 is an arbitrary clause) .

^This is somewhat oversimplified. Strictly speaking, a terminal element like Lois can only bear the Labels relation. Hence, minimally, Lois would be at least "one step removed" from the 1 relation. This node would bear the Labels rela­ tion to an element which bears the 1 relation to the clause in question. But even this would be an oversimplification, since it overlooks the internal structure of lexical items.

3.1. SPONSOR AND ERASE RELATIONS

61

(2) involves four linguistic states: (Si) = 1 (55, Lois) at L i ; (S2) = 2(55, John) at L-; (S3) = chomeur(55, Lois) at Lj; and (S4) = 1(55, John) at Lj. In terms of the relations Sponsor and Erase, the structure of (1) involves: (i) (Si) sponsoring (S3); (ii) (S3) erasing (Si); (iii) (S2) sponsoring (S4); and (iv) (S4) erasing (S2), i.e.: (3) Sponsor (1 (55, Lois) at L i , chomeur(55, Lois) at L j -) Erase (chomeur (55, Lois) at Lj , 1(55, Lois) at Lj) Sponsor(2 (55, John) at L i , (1 (55, John) at Lj) Erase (1 (55, John) at Lj, 2(55, John) at L i ). Note that in (3) all the states are unary. The intuitive content of the statement that linguistic state S m sponsors linguistic state S fl is that the occurrence of S fl is (partially) justified by, or is dependent upon, the occurrence of S m . And the intuitive meaning of the statement that lin­ guistic state S r erases linguistic state S g is that the occurrence of S g is sufficient for the nonoccurrence of S f in the phonologically relevant "surface aspect" of the sentence in question. In (3) above, the occurrence of state (S2) = 2 (55, John) at L i justifies (in part) the occurrence of state (S4) = 1(55, John) at Lj. And the occurrence of (S4) = 1 (55, John) at Lj is sufficient for the nonoccurrence of (Si) = 2(55, John) at L i in the phonologically relevant aspect of the structure of (1). (3) exemplifies a typical situation: where a linguistic state both sponsors and is erased by another linguistic state. In addition, (3) roughly and informally illus­ trates our conception of passivization. Other examples of Sponsor and Erase pairs include the following: (i) in so-called (Subject-to-Object) Raising constructions, a linguistic state involving a 1 relation sponsors, and is erased by, a state involving an "upstairs" 2 relation (see (16b) below), and (ii) in so-called Equi(NP-Deletion) constructions, a state involving an "upstairs" relation erases a state involving a "downstairs" 1 relation (see (21) below). In the latter cases, there is no sponsor relation between the two states in question, i.e., in Equi cases one state keeps another out of the "surface

62

3. ARC PAIR RELATIONS

structure" of a sentence, but neither state "justifies" the occurrence of the other. Informally then, we view a sentence as a pairing of two primitive rela­ tions, Sponsor and Erase, which hold between sequences of linguistic states. It is these two relations which constitute the essence of the grammatical structure of a natural language sentence. Hence, formal cor­ respondents to the informal Sponsor and Erase relations play a central role in the formalization of PN. Since arcs formally represent the content­ ful notion of sequences of trivially distinct linguistic states, the formal correspondents to Sponsor and Erase will take arcs as arguments. Each PN will consist essentially of two finite sets of ordered pairs of arcs, one set interpreted as a Sponsor relation, the other as an Erase relation. The formal correspondents to a Sponsor relation and an Erase relation will be termed Sponsor and Erase, respectively. To refer conveniently to an ordered pair of arcs which is either in a given Sponsor or Erase relation, we introduce the following: (4) Def. 43: Pair(A,B)

Sponsor(A, Β) ν Erase (A, B) .

Since two arbitrarily chosen sets of ordered pairs of arcs will not, in general, admit of a linguistically significant interpretation, one must im­ pose various constraints on such sets. The imposition and justification of strong, universal constraints of various sorts constitute a large part of this study. The goal is to arrive at an empirically adequate theory of uni­ versal grammar. While this is a task of staggering scope, the restrictions developed so far within the framework of APG mark, we believe, a valid first step toward realizing this goal. The numerous theorems proved in this work illustrate at once the desirability of developing a formal theory of APG and the relative "tightness" of even the current theory. Let us exemplify some basic constraints on pairs of sponsor and Erase relations. First, APG claims that a given linguistic state can be erased by only one linguistic state (formalized as The Unique Eraser Law in Chapter 5). A second restriction is that a linguistic state cannot erase

63

3.1. SPONSOR AND ERASE RELATIONS

a state which it sponsors (formalized as The No Infanticide Law in Chapter 5). Perhaps the most basic condition on Sponsor and Erase rela­ tions is that they both must be finite. It was previously stipulated that an R-graph is finite. One also wishes to require that the set of all arcs "in" a Sponsor and an Erase relation (that is, the arcs in the domains and ranges of Sponsor and Erase) representing the structure of a sentence in some language form an R-graph. The conjunction of this condition with the finiteness of R-graphs indirectly but effectively imposes the de­ sired finiteness on all such paired Sponsor and Erase relations, that is, on all PNs. Consider again (1). An approximation to part of the tion of it would be:

formal

representa-

ry

(5) Sponsor([2(55,"John)], [1(55, John)]) Erase ([1 (55, John)], [2(55, John)]) Sponsor([l (55, Lois)], [Cho(55, LOIS)]) Erase([Cho(55, Lois)], [2(55, John)]) ([Cho(55, Lois)< σ>], [1 (55, Lois)])| . Or consider (3.22). This is a PPN with the following members: (4) Sponsor = i(A, A), (B, B), (D, D), (E, E), (G, G), (A, C), (B, C)! Erase = I(C 1 B)J . It is often necessary to refer to the set of all arcs in the domains and ranges of the Sponsor and Erase relations of a certain PPN. For example, this set for (4) would be: (5) U,B,C,D,E,G| . For an arbitrary PPN, ΡΡΝ χ , such a set will be referred to as the Arc Set of PPN x •

To formalize this concept, we introduce three defined rela­

tions, Primary Arc Extractable, Secondary Arc Extractable, and Tertiary Arc Extractable. (6) Def. 47: Let (B, C) be an ordered pair of arcs. Then: Primary Arc Extractable (PAX) (A, (B 1 C)) (A = B) ν (A = C) . (7) Def. 48: Let X be a set of ordered pairs of arcs. Then: Secondary Arc Extractable(SAX)(A t X) «—» (3B)(3C)((B, C)f X λ PAX (A, (Β, C))). (8) Def. 49: Let ί Sponsor, Erase! be a PPN. Then: Tertiary Arc Extractable (TAX) (A, [Sponsor, Erase!) 1 «—» SAX (A, Sponsor) ν SAX (A, Erase) .

Analogous to Node-Extractable, discussed in Chapter 2, it is necessary to set up "extraction" relations to refer to arcs which play a role in the APG con-

4.1. S-GRAPHS

77

PAX permits formal reference to an arc which is either the first or second member of an ordered pair of arcs. SAX, defined in terms of PAX, allows one to refer to an arc which is either the first or second member of an ordered pair in some set of ordered pairs of arcs. The set of arcs SAX from a set of ordered pairs of arcs is the union of the domain and the range of that set. TAX permits one to conveniently refer to an arc which is SAX from either Sponsor or Erase of some PPN. With these tools, the informal notion Arc Set of a PPN is easily formalized: (9) Def. 50: Let X be a PPN. Then: A e Arc Set (X) "A is a member of the arc set of X" TAX (A, X) . The Arc Set (ΡΡΝ χ ) is extensionally equivalent to the union of the fields of the sponsor and erase relations of ΡΡΝ χ . A field, to paraphrase

Carnap (1958: 72), is the class of all members of a binary relation, R, where a member of R is an element which is either the first or second member of some ordered pair in R . We make explicit here another convention used in the formalism. Un­ less otherwise indicated, arcs referred to in laws, definitions, and theo­ rems are assumed to be members of the arc set of an arbitrary PN, defined below, rather than of, e.g., an arbitrary L-graph, S-graph, etc. At this point, we restrict attention to a specific type of arc set, name­ ly, those which are also R-graphs. This will in turn allow us to define "S-graph" and "L-graph." Focusing first on the concept S-graph, and pro­ ceeding inductively, we initially define the notion Surface Arc. These are arcs in the arc set of a PPN which are not erased. For example, A, C, D, E, and G of (5), which form an R-graph, the arc set of (4), are

structs PPN and PN. This is a result of not having defined these formal objects as triples consisting of (i) a set of arcs, (ii) a Sponsor relation, and (iii) an Erase relation. While the latter approach would allow one ίο refer to arcs with just set membership, it is less convenient in other respects than that adopted in the text.

78

4. PAIR NETWORKS

all surface arcs. On the other hand, B of (5) is not, since it is erased by C. Given the notion Surface Arc, we then introduce the concept of the set of all surface arcs of an R-graph, called the Surface Arc Set of that R -graph. (10) Let Q be an R-graph which is the arc set of some PPN. Then: a. Def. 51: Surface Arc(A) «--> AeQ λ Not ((3B)(Bf QAErase (B, A))) b. Def. 52: A e Surface Arc Set (0) «--> AeQ

A

Surface Arc(A) .

To illustrate, the surface arc set of (5) is: (11) ί A, C, D, E, Gi . The notion Surface Arc Set is important since an S-graph will simply be a surface arc set meeting six restricting conditions. These are roughly as follows. First, an S-graph, like an R-graph, must be nonempty. Second, each nonterminal node node-extractable from a given S-graph must R-govern (in the S-graph) a phonological node. Therefore, an S-graph has no "dangling" nonterminal nodes. Third, an S-graph must be pointed. Fourth, there is a certain class of nodes, called Quasi-Roots, which must be node labeled Cl . The concept Quasi-Root

is discussed in detail below. Fifth, the set of arcs of a surface sentence, excluding L and LP arcs, must be a tree (in the graph-theoretic sense;

see below). Finally, S-graph phonological terminations cannot be neigh­ bors. Any surface arc set meeting these six conditions is an S-graph. For illustration, consider (12a) and its PPN, ignoring LP arcs and sponsors for L arcs, (12b). 2 (12) a. John wants to be kissed by Lois.

Coordinate sequences are also ignored. Throughout this work, we allow our­ selves the freedom to suppress coordinates without explicit mention.

4.1. S-GRAPHS

The arc set of (12b) is Q =

{A, B,

79

C, D, E, G, H, I, J1, J 2 , J 3 , J 4 ,

J5, J6, J7,J9,J10,J11,J13,J14,J15,K,M,N,O,Q,R,S}.This set forms an R-graph, as the reader can verify. The Surface Arc Set of Q is {A, B, C, G, J 1 , J 2 , J 3 , J4, J 5 , J 6 , J 7 , J g , J10, J 1 1 , J13, J 1 4 , J 1 5 , K, M, N, O, Q, R, Si, or diagrammatically.

80

4. PAIR NETWORKS

(13)

WANT

want(s)

Cho

KISS

GR,

(to) (be) kissed

Nom

GRw Nom

John Lois

With respect to the informal conditions previously specified for S-graphs, (13) evidently satisfies the first three since (i) it is nonempty, (ii) each nonterminal node in it R-governs a phonological node, and (iii) it is pointed. Although this cannot yet be verified, only node 9 is a quasiroot and, in accord with the fourth S-graph condition, it is labeled Cl. Finally, as will be verifiable shortly, the set of non-L and non-LP arcs, iA, B, C, G, K, M, N, 0, Q, R, Si, forms a tree. Hence, (13) is an S-graph. 3

3 Note that logical nodes, like WANT in (13), occur in S-graphs. This is dis­ cussed further below.

4.1. S-GRAPHS

81

Before defining "S-graph" formally, it is necessary to introduce sev­ eral additional concepts, including (APG) Chain and (APG) Cycle. We take this opportunity to define related concepts needed for the forma'lization of L-graph. A chain is a sequence of arcs such that adjacent arcs are attached. The "direction" of the arcs is irrelevant, i.e., adjacent arcs may overlap, be neighbors, or be a branch/support pair. Both (14a, b) are chains:

(ABCDEFGH)

(ABCOE)

An (APG) Path is a sequence of arcs such that the first of an adjacent pair of arcs is the support of the second. In a path, the "direction" of the arcs is significant. (14b), but not (14a), is a path. An (APG) Cycle is a chain where the last arc in the sequence is attached to the first arc, (15a, b) are both cycles:

(ABCDEGH)

b.

(A B C DE GHI)

82

4. PAIR NETWORKS

An (APG) Circuit is a path where the last arc in the sequence is a support of the first arc. For example, (15b), but not (15a), is a circuit. Formal definitions of these concepts are given in (16).

Note that according to our conventions

in each case

represents a sequence of arcs. Given the concept Cycle, it is possible to define the notion Tree, mentioned in Chapter 2. Our notion Tree is equivalent to the typical graph-theoretic concept of the same name, except that the latter is normally defined on undirected graphs, whereas the current notion is specified in terms of sets of arcs, which are basically directed graphs. A set of arcs is a tree if and only if the set is connected and contains no cycles. The familiar linguistic objects known as "constituent structure trees" in transformational linguistics are not equivalent to trees in the present sense, for two reasons. First, the dominance and precedence relations of "constituent structure trees" almost always form cycles. This is readily apparent if one makes explicit the precedence relation (as we did in a different context for (2.58) and (2.59)), rather than relying on the informal notational device of left-right orientation. For example, using "Dom" for the dominance relation, dashed lines for the precedence relations, and

4

Compare these definitions with their analogues in Berge(1973: 7-8).

83

4.1. S-GRAPHS

"Lab" for the Labels function, the "constituent structure tree" in the terms of Wall (1972) for John slept is roughly:®

John

slept

Note that the lines in (17) are not APG arcs. Further, the Dominance re­ lation of (17) alone does form a (graph-theoretic) tree. Second, a graphtheoretic tree need not have a single root, and this is also true for our directed graph analogue of that notion. A single-rooted tree in graphtheoretic terminology is sometimes called an Arborescence. For example, ignoring the differences between directed and undirected graphs, (18) is a tree in the graph-theoretic, but not the constituent structure, sense:

^Dominance lines predictable from the transitivity of dominance are omitted from (17). Only nodes in immediate dominance are actually connected by lines in (17).

84

4. PAIR NETWORKS

In order to formally define the APG directed graph version of "tree," we first introduce the notion of a sequence of arcs being a "sequence in a set of arcs, X." This relation holds between a sequence of arcs, S, and a set of arcs, X, just in case every arc of S is a memfeer««f X. (19) Let X be a set of arcs and (A 1 ··· A ffl ), m > 0 , a sequence of arcs. Then: a. Def. 57: Sequence ((A 1 • • • A ffl ), X) (Vi, l Node-Extractabie (a, Q)

Λ

Not (Node-Extractable(a, S-graph (Q))). (32) Def. 64: (Node) Deleted (a) ^ (3Q) (R-graph (Q)

Λ

Node-

Extractable (a, Q) A Not (Node-Extractable (a, S-graph (Q)))).

For example, VN in (3.10b) and el in (3.11b) are both deleted, since erased arcs do not appear in S-graphs. Ultimately, one wants to strictly

4.1. S-GRAPHS

91

control the class of deleted nodes, which is much more restricted than the class of heads of erased arcs (see Chapter 9). 4.2. L-graphs We now discuss the notion L-graph. First, a caveat is in order. We have not had the opportunity to study this aspect of APG in depth and, in­ dependently of this, there are, of course, many long-standing mysteries concerning so-called logical form. For example, it is not clear to us how names should be handled. In previous examples, the representation of a name included only a phonological node. On the other hand, the repre­ sentation of lexical items like Wss included a grammatical category node, a phonological node, and a logical node (see (13)). This reflects our pro­ visional view that the postulation of logical nodes for names is superflu­ ous. Thus, L-graphs will contain terminal nodes which are not logical nodes. In other words, the logical representation of a name is the phono­ logical node corresponding to that name. Since this is a matter we have not investigated in detail, we merely note our current assumptions. Another obstacle to completely characterizing L-graphs involves our view that superficially simplex nominals like John and man have complex, ill-understood representations, involving the same logical structures as restrictive relative clauses. For example, under this view, the L-graph representation of John would, roughly, be the same as that of the one named John. Moreover, under our view, to adequately reflect logical structures, it is likely that restrictive relative clauses involve a predicate of identification, represented in (35) below as a two place predicate, IDENTIFY, and that such clauses are not, in L-graphs, embedded in nominal constituents. Thus, for example, the PN of (33) would involve (34) and (35). (33) The one who is named John runs.

92

4. PAIR NETWORKS

(34)

8

runs Det

The

one

John

named

An approximation to the L-graph associated with (33) would be: (35)

GR GR z. RUN

IDENTIFY

Det

NAMED

JOHN

THE

An important aspect of (35) for present purposes is that, unlike (34), where A and B form a (bi)circuit, (35) contains no circuits. As discussed

93

4.2. L-GRAPHS

later, we postulate that L-graphs cannot contain circuits. If (34) and (35) are "collapsed," we arrive at a first approximation to the entire R-graph for The one who is named John runs: (36)

RR

GR^ GR-

IDENTIFr

Stem RUN John

runs

Stem

Det

NAMED GR1

The

one named

The clause with predicate IDENTIFY in (36) is essentially equivalent to a "such that clause." The meaning of (36) can be paraphrased by: (37) The χ (such that [ χ is named John] identifies x) runs. (37) mirrors the formal properties postulated for sentences like (33). In particular, what looks superficially like a relative clause with main predi­ cate NAMED is embedded under the binary predicate IDENTIFY. Further, there is a condition of identity holding, e.g., between the subject of the upstairs predicate, RUN, and the subject of the clause with predicate NAMED, embedded under IDENTIFY. Justasarcs G, C, and A must overlap in (36) for a logically coherent structure to result, the relevant arguments of a "sueh that sentence" must be identical, e.g.:

94

4. PAIR NETWORKS

(38) a. *The person such that he is named John identifies bagels. b. *The χ such that y is named John identifies ζ. This shows, basically, that structures like (35) exist independently of our theoretical assumptions regarding the logical structures of sentences like (33). Skipping a number of unresolved questions, we regard the existence of "such that clauses" like the one in (37) as increasing the plausibility of our analysis of sentences like (33). Of course, we have yet to specify the sponsor and erase pairs which mediate between the S-graph and L-graph associated with (33). Focusing on (36), C and E must be erased and, presumably, an arc other than B sponsors B , perhaps C . However, we will not pursue this matter be­ yond this point, leaving to future research the problems related to the logi­ cal representation of sentences like (33). Turning to the task of characterizing L-graph, we first define the more general notion of the Logical Arc Set of an R-graph, Q . The Logical Arc Set of Q is the set of all arcs in Q which (i) sponsor themselves and (ii) whose R-signs are members of the set of "logical" R-signs, LR, i.e., the set of R-signs claimed to play a role in so-called semantic or logical representation. An L-graph is a logical arc set meeting certain conditions. To define "Logical Arc Set of Q " formally, we introduce two further concepts: {39) a. Def. 65c Self-Sponsor(A) *-» Sponsor (A, A). b. Def. 66: Logical arc (A) Self-Sponsor(A)ALR arc (A). c. Def. 67: Let Q be an R-graph which is the arc set of some PPN. Then: A £ Logical Arc Set(O) Not (Logical Arc(A)) . Proof. Assume that Replace(A', B'). It follows from Theorem 9 that A'^ B', i.e., that: (i)

D-Sponsor (B', A') .

Suppose, contrary to the consequent, that A' is a logical arc. Then from the definition of the latter concept (see (4. (39b))), it would follow that: (ii) Self-Sponsor (A') . But the conjunction of (i) and (ii) contradicts PN law 4. QED. One can also show that: (25) THEOREM 11 (The Successor Nonlogieal Arc Theorem) Successor (A, B) -» Not (Logical Arc(A)) . Proof. The proof is essentially identical to that for Theorem 10 except that the analogue of (24i) follows from the definition of "Successor" rather than from Theorem 9. QED. Consequently, with respect to S-graphs and L-graphs, we know over­ all about replace and successor situations that (i) successors and replacers can, but need not be, surface arcs; (ii) predecessors and replacees can, but need not be, logical arcs; (iii) that predecessors and replacees cannot be surface arcs; and (iv) that successors and replacers cannot be logical arcs. Next, we consider certain similarities and differences between Succes­ sor and Replace. The former only holds between overlapping arcs. Indeed, the successor relation is one of the two "sources" of overlapping structural arcs permitted by APG (the other being overlapping self-sponsoring arcs,

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

119

see Theorems 116, 118, and 119 of Chapter 11). On the other hand, Re­ place never holds between overlapping arcs: (26) THEOREM 12 (The Replace Nonoverlap Theorem) R e p l a c e ( A 1 B ) -» N o t ( O v e r l a p ( A , B ) ) . P t o o f . Assume that Replace (A', B'). It follows from the definition of

"Replace" that B' sponsors A' and from Theorem 9 that A'^ B'. Hence, if, contrary to the consequent, A' and B' overlap, A' is a successor of B', contradicting the fact that A' is an entrant, which is guaranteed by

the definition of "Replace." QED. Thus, while Successor is a fundamental relation between overlapping arcs, Replace connects only nonoverlapping arcs. A further significant difference between Replace and Successor in­ volves R-signs. Recall that the replace relation involves local sponsor­ ship between arcs with identical R-signs. The definition of "Successor" itself says nothing about R-sign. Moreover, there is no completely gen­ eral restriction precluding arcs with the same R-sign from being in the successor relation. Thus, we want to allow, for many languages, comple­ ment clause 2 arcs to have main clause 2 arc successors (these are cases where 2s undergo raising, see Trithart [1976] for an example from Chichewa). However, we do not want to allow local successors to have the same R-sign as their predecessors. For this would say of natural lan­ guages, under the interpretation of the formalism, that, in effect, identical states could be ancestors. (But see Chapter 6, section 6.) We hence im­ pose a further constraint on successorhood: (27) PN Law 5 (The Local Successor Distinct R-Sign Law) Successor (A, B) -» Not (Facsimile (A, B)) . Given (27), local successors are in a sense opposite to replacers in that they can never share R-signs with their local sponsors, while replacers must

be facsimiles of one of their sponsors.

120

5. BASIC SPONSOR AND ERASE LAWS

Turning to some similarities between Successor and Replace, we have observed that both are irreflexive, Successor by definition and Replace by virtue of Theorem 9. We would like both these relations to be asymmetri­ cal as well. If A is a successor of B, it should not be possible for B to be a successor of A, and if A replaces B then B should not be able to replace A. So far, however, nothing guarantees these properties, which are necessary, inter alia, to make these formal relations reconstruct the notions of successor chain and replace chain holding between linguis­ tic states, as discussed in Chapter 1. We can impose asymmetry of these relations by imposing it more generally on the primitive Sponsor relation which underlies them. (28) PN Law 6 (The Sponsor Independence Law) D-Sponsor(AjB) h> Not(R-Sponsor(B, A)) . This law adds content to certain aspects of our informal interpretation of the Sponsor relation, namely, that Sponsor (A, B) means that the existence of A is a necessary condition for the existence of B . (28) specifies that one arc can only justify the existence of a distinct second arc if its own existence is justified independently of that second arc. An immediate consequence of (28) is: (29) THEOREM 13 (The No Mutual Sponsorship Theorem) D-Sponsor (A, B) -> Not (Sponsor ( B , A)) . Proof. Immediate from PN law 6 since sponsorship is a special case of R-sponsorship. QED. It is then evident, as desired, that: (30) THEOREM 14 (The Successor Asymmetry Theorem) Successor(A, B) -» Not (Successor (B, A)) . Proof. Immediate from Theorem 13. QED.

And it is also evident that:

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

121

(31) THEOREM 15 (The Replace Asymmetry Theorem) Replace (A, B) -» Not (Replace (B, A)) . Proof. Immediate from Theorem 13. QED. In Chapter 11 we define the notion Lineage, a set of arcs consisting of all and only an entrant and its R-successors. Theorem 14 guarantees that a lineage forms a unique sequence of distinct arcs with the entrant as first member, its successor, if any, as second, etc. That is, Theorem 14 guarantees that the formal notion Successor yields a reconstruction of the intuitive idea that certain sets of overlapping arcs form chains with an original member and its descendants. A further similarity between Successor and Replace is that both are obviously incompatible with self-sponsorship: (32) THEOREM 16 (The Self-Sponsor Nonsuccessor Theorem) Self-Sponsor (A)

Not(JCSB) (Successor (A, B))) .

Proof. Let A' be self-sponsoring and assume contrary to the theorem that there is some arc, say B', which is a predecessor of A'. It then follows from the definitions of "Successor/Predecessor" that B' D-sponsors A', contradicting The Self-Sponsor Law, which does not per­ mit self-sponsoring arcs to have D-sponsors. QED. (33) THEOREM 17 (The Self-Sponsor Nonreplace Theorem) Self-Sponsor ( A) -» Not ((3B) (Replace (A, B))) . Proof. The proof is essentially identical to that for Theorem 16 except that the conclusion that B' D-sponsors A' follows from Theorem 9 rather than from a definition. QED. Next, neither the definitions of "Successor" or "Replace" nor any theorem so far indicates that these notions are unique, i.e., such that any arc has at most one successor or one replacer. However, we want both of these to be consequences. With respect to replacers, the result can be proved from previous assumptions:

122

5. BASIC SPONSOR AND ERASE LAWS

(34) THEOREM 18 (The Replacer Uniqueness Theorem) Replace (Α, Β)

Λ

Replace (C, B) -> A=C.

Proof. Suppose that B' is replaced by both A' and C'. It follows from The Replacer Erase Law that: (i) Erase (A', B')

A

Erase (C', B').

But (i) contradicts The Unique Eraser Law unless A' = C'. QED. To show that successorhood is unique is more complicated and de­ pends on two further PN laws we now introduce. We have illustrated cases where arcs have one sponsor and where arcs have two sponsors, but we have not given illustrations either here or in Chapter 3 of cases where a single arc has 3, 4, 5, 11, 848, 90,000, etc., sponsors—all logical­ ly possible situations. This is, we claim, not fortuitious since a basic constraint on the sponsor relation, corresponding to the numerical limita­ tion on Erase imposed by The Unique Eraser Law, is that no arc can have more than two sponsors: (35) PN Law 7 (The Maximal Two Sponsor Law) Cosponsor (A, B, C)

A

Sponsor(DjC) ^ D=AvD=B.

It is now evident that every arc has one or two sponsors. First of all, unisponsored arcs have one sponsor, not by definition, since we defined "Unisponsored" as the negation of Cosponsor. Rather, this is provable, because not having two distinct sponsors leaves a unisponsored arc with either one or zero sponsors. But The PN Sponsor Condition requires every arc to have a sponsor, eliminating the latter possibility. If then an arc is not unisponsored, it is cosponsored, it then following immediately from PN law 7 that it has two sponsors. Just as The Unique Eraser Law imposes no constraint on the number of arcs some specified arc can erase, The Maximal Two Sponsor Law im­ poses no constraint on the number of arcs some fixed arc can sponsor. We know of cases where a single arc apparently sponsors three, four, or more

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

123

other arcs.4 We also know of cases where a single arc erases at least three other arcs.5 Consequently, it is unclear whether there are any laws to be stated about this aspect of these relations in general. However, be­ low we consider constraints on a special case for the erase relation. There is a further new law needed to prove the uniqueness of succes­ sors, one which determines the second sponsor of a replacer which re­ places an arc with a successor: (36) PN Law 8 (The Predecessor-Replacer Sponsor Law) Successor (Α, Β) Λ Replace(C,B)

Sponsor(AiC) .

This principle says that an arc which replaces (and hence is sponsored by) a predecessor has as second sponsor the successor of that predecessor. Thus, in such cases, it is arcs in a predecessor/successor pair which form the cosponsoring pair required by the definition of "Replace." Considera­ tion of replacer arcs B in (14b) and C in (18) will show that these meet the antecedents of (36) and the consequent as well. Thus, C in (18) re­ places the predecessor of A , B , and is cosponsored by A. PN law 7 therefore says that the situation in, e.g., (14b) and (18) is not accidental. With the apparatus introduced so far, one can show that: (37)

THEOREM

19 (The Successor Uniqueness Theorem)

Successor (Α, Β)

Λ

Successor (C, B) -> A = C .

^For example, in our analysis of so-called clause union constructions, there is invariably a U arc whose head corresponds to the complement clause predicate, and, roughly, this U arc sponsors one neighboring arc for each final stratum (see Chapter 8, section 6) nominal dependent of the complement. Hence, if that com­ plement has three, four, or five dependents, the U arc will sponsor three, four, or five arcs. Xn a French example like: (i) J'ai fait donner Ie livre a Marie par Jacques. I have made give the book to Marie by Jacques = "I had the book given to Marie by Jacques." the U arc, whose head corresponds to donner, sponsors three main clause arcs, w h o s e h e a d s correspond t o t h e n o m i n a l s Ie l i v r e , Marie, a n d J a c q u e s . ^See example (5.39) in the text below.

124

5. BASIC SPONSOR AND ERASE LAWS

Proof. Suppose, contrary to the theorem that Successor(A', B') and Suc­

cessor^', B') and A'^ C'. There are two cases to consider: Case (a): Suppose that B' has no replacer. Then, by The Successor Erase Law, both A' and C' erase B', violating The Unique Eraser Law. Case(b): Supposethat B' has a replacer, D'. The Predecessor Replacer Sponsor Law entails that both A' and C' sponsor D'. But from the definition of "Replace," it follows that B' also sponsors D'. Moreover, A'^ C', and since these are successors of B', neither can be identical to B' either. Hence, D' has three distinct sponsors, contradicting The Maximal Two Sponsor Law. QED. Theorems 18 and 19, which show the uniqueness of replacers and suc­ cessors, do not thereby show the uniqueness of replacees and predeces­ sors. Nothing yet indicates either: (38) a. Replace (Α, Β)

Λ

Replace (A, C) -> B=C

b. Successor (Α, Β) Λ Successor (A, C) -» B = C . It turns out that a demonstration of (38b) depends on many additional assumptions and the proof must be delayed until further apparatus is available (see Theorem 65 of Chapter 8). To prove (38a), one must also apparently appeal to further laws. At the moment, all that is known about situations meeting the antece­ dent of (38a) is that the single replacer erases its two distinct replacees and sponsored by both of them, all three being facsimiles. None of these conclusions yields any contradiction. It seems then that to prove (38a) one must guarantee that nonunique replacees violate some law about the number of arcs a single arc can erase. 6 We observed above that there was 6 An alternative line of attack on this question would posit a general law of stratal uniqueness for all arcs capable of having replacers. For the coordinate principles of Chapter 6 (see The Replacer Coordinate Law) guarantee that (38a) could be violated only if a single stratum contained two arcs with the same R-sign. However, it is unclear whether any such principle can be maintained, it being possible for a single stratum to contain, e.g., more than one Cho arc. This is the case for instance in examples like (i) and (ii), where the underlined nominals head final stratum Cho arcs:

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

125

apparently no completely general constraint on this. For example, in the sentence: (39) While holding her breath, Mary attempted to submerge and then to seize the rock. the 1 arc of the attempt clause erases the 1 arc of its complement, the 1 arc of the while clause, and the 1 arc of the then clause, three in all. However, in such cases, there is so-called "coreference." In current terms, these erasures involve overlapping arcs, unhooking in the sense of definition (8b) above.7 We thus know of instances where one arc assassinates more than one arc, but in all these it is apparently the case that at most one of the erase pairs is a zeroing pair. We conclude that there is the possibility of imposa law limiting the number of nonoverlapping arcs a single arc can erase to exactly one: (40) PN Law 9 (The Multiple Assassin Law) Zeroes (Α, Β) Λ Assassinate (A, C) -> Overlap (A, C) . Given this law: (41) THEOREM 20 (The Replacee Uniqueness Theorem) Replace (Α, Β) Λ Replace (A, C) -» B = C . Proof. Assume that Replace (A', B') and Replace (A', C') and, contrary

to the consequent, that B ^ C'. It follows from the definition of "Replace" and Theorem 9 that: (i)

D-Sponsor(B", A")

A

D-Sponsor(C', A').

(i) Melvin was given the book by Ted. (ii) It is believed by Fred that goats are telepathic. 7 PNs where one arc erases both an overlapping and a nonoverlapping arc are found, e.g., in the case of short passives like: (i) Melvin was tickled. Here the successor 1 arc erases its predecessor 2 arc, these necessarily over­ lapping, and also erases the initial 1 arc, these not overlapping. For discussion of such cases, see Chapter 9.

126

5. BASIC SPONSOR AND ERASE LAWS

Now, if either B' or C' overlapped A', A' would be a successor, con­ tradicting the fact guaranteed by the definition of "Replace" that A' is an entrant. Hence: (ii) Not (Overlap (A', B')) λ Not (Overlap (A', C')) · But The Replacer Erase Law entails that A' erases both B' and C'. Given (ii), this contradicts PN law 9 since A' would be zeroing two dis­ tinct arcs. QED. Given that we later prove the uniqueness of predecessors (see Theo­ rem 65 of Chapter 8), APG provides an extremely tight theory of both the Successor and Replace relations and their converses. Every successor has a unique predecessor and conversely, and every replacer has a unique replacee, and conversely. These are particularly important results from the point of view of coordinate determination, considered in the next chap­ ter. There principles are given which, inter alia, determine the possible first coordinates of replacers and local successors on the basis of, re­ spectively, the last coordinates of replacees and predecessors. In the absence of uniqueness for predecessors and replacees, these laws would yield inconsistent results. Next, in this introductory discussion of Successor and Replace, we make explicit the obvious consequence that these two relations are mutual­ ly exclusive: (42) THEOREM 21 (The Replacer/Successor Incompatibility Theorem) ReplaceC A, B) -» Not (Successor (A, B)) . Proof. Immediate from the definition of "Replace" which requires a replacer to be an entrant, and hence an arc with no predecessor. QED. It is common for an arc, A, sponsored by B to erase B. This happens, as we have seen, when A is a successor and even more gener­ ally when A is a replacer. There are other cases. We know, however, of no circumstances in which an arc A sponsors an arc B and also erases B, except in the degenerate case where A = B. We hence im­ pose this as a law:

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

127

(43) PN Law 10 (The No Infanticide Law) Sponsor(A, B) -» Not (Assassinate (A, B)) . By using Assassinate, we eliminate the case where A and B ate identi­ cal. From (43) two further theorems about Successor and Replace follow: (44) THEOREM 22 (The Successor Infanticide Theorem)

Successor (A, B) -> Not (Assassinate (B, A)) . Proof. Immediate from the definition of "Successor" and PN law 10. QED. (45) THEOREM 23 (The Replacer Infanticide Theorem) Replace(A l E) -» Not(Assassinate(B, A)) . Proof. Immediate from the definition of "Replace" and PN law 10. QED. As we have seen, there are two types of erasure of predecessor arcs. These ate erased by their teplacers if they have such, ot by theit succes­ sors otherwise. These two erasure cases illustrate the difference between zeroing and unhooking. Since teplacers do not overlap the arcs they re­ place, they zero them. However, since successors by definition overlap their predecessors, when they assassinate them, they unhook them. There ate evidently two types of unhooking of predecessors by succes­ sors, local unhooking for local successors and foreign unhooking for for­ eign successors. In the case of local unhooking, what is involved is the assassination of one of two parallel arcs by the other. A question arises about the scope of unhooking when successors are not involved. It is cer­ tainly easy to find situations where foreign unhooking must be recognized in our terms. This is the case, for instance, in our treatment of phenomena discussed in TG terms under the rubric of Equi constructions. Thus, in an example like: (46) Melvin wants to sing. the self-sponsoring 1 arc of the main clause unhooks the overlapping selfsponsoring 1 arc of the complement, as indicated in the partial PN:

128

5. BASIC SPONSOR AND ERASE LAWS

(47)

Melvin

(to) sing

wants

While in an example like (48), the self-sponsoring 1 arc of the main clause unhooks the 1 arc local successor of a 2 arc, which defines a passive clause, as indicated in the PN fragment in (49). (48) Melvin wants to be praised by Lucille. (49)

wonts

Melvin

(by) Lucille

Thus

foreign

(to) (be)praised

unhooking riot pairing successors and their predecessors

seems well attested. One might expect then that similar cases of unhooking could be found where the paired arcs are neighbors, that is, unhooking by A of a parallel arc B , where A is not a successor of B . Thus, one might analyze examples like (50a) as involving unhooking of a self-sponsoring 2 arc by a parallel self-sponsoring 1 arc: (50) a. Melvin shaved. b. Melvin shaved himself.

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

129

This would yield a partial PN of the form: (51)

shaved

Melvin

However, we claim that this is an impossible analysis for cases like (50a). We embody this claim in the principle: (52) PN Law 11 (The Parallel Assassin Law) Assassinate(A 1 B)

Λ

Parallel (A, B)

Successor(AjB) .

This law leaves it possible for foreign unhooking not to involve successor/ predecessor pairs, as in (47) and (49). But it blocks local unhooking in­ volving nonsuccessors, and hence, local unhooking between self-sponsoring arcs, as in (51). Therefore, with respect to cases like (50a) we are, in effect, reduced to an analysis in which the erased 2 arc is a nonsurface arc for the same reason it is a nonsurface arc in cases like (50b): it has a replacer. The difference between (50a, b) must then reside in the fact that (50a) involves, in addition, erasure of the arc whose head corresponds to the pronoun which is part of the S-graph of (50b). Hence (50a) would, given PN law 11, have to have a representation of the form:

Mfelvin

f himself

t shaved

130

5. BASIC SPONSOR AND ERASE LAWS

Here A and B cosponsor the replacer C, C erasing B as required by The Replacer Erase Law. (53) yields (50a) and not (50b) only because C self-erases.

The virtue of The Parallel Assassin Law vis-a-vis cases like (50a) is that it (i) eliminates what would otherwise be the possibility of two dis­ tinct analyses (that is, (51) alongside of (53)), and (ii) forces the erasure of the (in this case) self-sponsoring 2 arc in (50a) to be a function of the independently needed apparatus (i.e., The Replacer Erase Law) which yields the erasure of the self-sponsoring 2 arc in cases like (50b).8 As will be clear from Chapter 6, structures like (51), now blocked, are incom­ patible with an otherwise invariant property of arcs with local assassins. Namely, these arcs can never be members of the final "level" (technically, stratum) of the constituent corresponding to their tail node. As clarified

in the discussion of The Fall-Through Law in Chapter 6, having a local assassin is the only means permitting an arc which is in "level" i not to be in the next "level," i+1. Thus, local assassination always keeps an arc out of the final "level." However, cases like (51) would define single "level" structures in which a locally assassinated arc is in the necessarily final "level." Moreover, the fact that structures like (51) are blocked by PN law 11, leaving (53) as the only type of relevant structure for the examples in question, is consistent with the fact that structures like (51) also violate PN law 27 below. The latter principle establishes a connection between the coordinates of arcs related by Local Assassinate, a connection re­ quiring the assassin to have a first coordinate greater than the last coordi­ nate of the erased arc. This condition cannot be met in cases like (51).

One could of course apply the same logic to apparent cases of foreign assas­ sination involving overlapping arcs, i. e., attempt to reduce equi cases to erasure of nonoverlapping (pronominal) arcs. However, we suspect that this is incorrect in general. There are cases where, e.g., equi structures cannot be properly analyzed in terms involving in effect pronoun deletion. See Postal and Pullum (1978: section 6) for one involving English complementizer contraction.

5.4. PROPERTIES OF SUCCESSOR AND REPLACE

131

Hence, to the extent that PN law 27 is well motivated, there are grounds independent of PN law 11 for believing structures like (51) nonexistent. It would be natural to investigate the possibility of deriving PN law 11 as a theorem from assumptions including PN law 27. However, as far as we have been able to determine, this is not possible. The distinction between foreign unhooking and the more restricted possibilities for local unhooking imposed by PN law 11 is connected to the fact that the determinants of coordinates for an arc, which determine "levels," are basically limited to neighbors of the arc in question. Hence, foreign unhooking, like foreign assassination in general, even if unre­ stricted, will not interact with the principles determining the first and last coordinates possible for arcs. 5.5. A fundamental arc typology We claim that natural language grammar is organized around a basic typology of arcs, which serves as the basis for a number of laws governing Sponsor and Erase. This typology involves three basic types of arc, re­ ferred to as domestic arcs, immigrant arcs, and grafts. These types ex­ haust the class of arcs. Domestic arcs have parallel sponsors: (54) Def. 84: Domestic(A) (3B) (Sponsor (Β, Α) Λ Parallel (A, B)) . It follows from (54) that a domestic arc is either: (55) a. an arc which is self-sponsoring, or b. an arc with a distinct parallel sponsor, i.e., a local predecessor More precisely: (56) THEOREM 24 (The Domestic Nonself-Sponsoring Arc Theorem) Domestic(A)

A

Not (Self-Sponsor (A)) -+ (ΉΒ) (Local Successor( A, B)) .

Proof. Let A' be a domestic nonself-sponsoring arc. It follows from the definition of "Domestic" that A' has a parallel sponsor, say B'. Therefore,

132

5. BASIC SPONSOR AND ERASE LAWS

since A' overlaps and is distinct from B', it is a successor of B', and since it is a neighbor, it is a local successor. QED. In the partial illustration of the structure of a simple passive clause given in (3.7) above, repeated with simplifications as (57), all of arcs A-E are domestic.

John

(by) Lois

(was) kissed

B, D, and E are of type (55a), while A and C are of type (55b). Next, we introduce the class of arcs which are intrusive. This is simply the complement, within the set of arcs, of the set of domestic arcs: (58) Def. 85: Intrusive(A) (3B) (Foreign Successor (A, B)) . That is, an immigrant is an arc with a nonlocal predecessor, hence one nonlocal sponsor. The definition of "Immigrant" guarantees that immigrants

5.5. A FUNDAMENTAL ARC TYPOLOGY

133

meet the requirement on all arcs of having at least one sponsor. However, the definition is silent on an upper limit for the sponsors of such arcs. It does not indicate whether all immigrants have one sponsor, whether some have one sponsor and some two, or whether all immigrants have two spon­ sors. While this is a question where a certain doubt remains, we have constructed the present version of APG theory on the assumption that all immigrant arcs have two sponsors, one of which is local. Our basic grounds for this involve assumptions about coordinate determination, namely, that this is based on the relation between an arc and its neigh­ bors. Without a local sponsor, there would be no way consistent with this principle to specify the first coordinates of immigrant arcs in a general way. It also seems to us that in the clear cases of immigrants, there is some unique neighbor of the immigrant which is a necessary condition for the existence of the immigrant. And we have assumed exactly that to say A sponsors B is to say that A is a necessary condition for the exis­ tence of B. Hence we propose: (60) PN Law 12 (The Immigrant Local Sponsor Law) Immigrant(A)

(3B) (Local Sponsor (B, A)) .

It follows from the definition of "Immigrant" and other assumptions that an immigrant arc is intrusive: (61) THEOREM 25 (The Immigrant Intrusiveness Theorem) Immigrant(A) -» Intrusive(A) .

However, we delay a proof of this until Chapter 8, section 2, since it de­ pends on The Predecessor Uniqueness Theorem, which is only proved there. The definition of "Immigrant" and PN law 12 specify that an immi­ grant arc has a foreign predecessor and a local sponsor, which, given the uniqueness of predecessors, cannot be a predecessor. Hence, an immi­ grant arc has one overlapping foreign sponsor and one nonoverlapping local sponsor.

134

5. BASIC SPONSOR AND ERASE LAWS

The notion Immigrant is illustrated by the partial representation in (63) of the English raising sentence in (62): (62) Melvin is believed by Ted to know French. (63) Chtf (is) believed Cho,

(by) Ted

Melvin

French

(to) know

In this structure, D is the immigrant arc. That is, it is a foreign succes­ sor of I, which it erases because there is no replacer. This all follows since I and D are not neighbors, they overlap, and I sponsors D. PN law 12 then requires that D have a local sponsor as well as its foreign predecessor. This condition is met since E also sponsors D . We remarked earlier that local sponsors for immigrants were partially justified by the fact that neighbors of immigrants seemed necessary to justify them. In this case, as is well known, the raising phenomena in question is limited to verbs with certain kinds of complements, in our terms, complements corresponding to the heads of 2 arcs. It is thus natu­ ral that these 2 arcs sponsor the immigrants they permit. In RG terms, the head of the 2 arc E would be the host for the rais­ ing of Melvin. Hosts are then, in APG terms, heads of local sponsors of immigrant arcs, where the predecessor of the immigrant is in the constitu­ ent determined by the head (see Chapter 7, for an account of constituents, and Chapter 14, section 6 for further elaboration of immigrant local sponsors). Since (63) is a passive structure, D , whose R-sign is 2, sponsors a 1 arc, C, which is its local successor. However, C has a parallel

135

5. 5. A FUNDAMENTAL ARC TYPOLOGY

sponsor, namely, D, and is thus domestic. A, B, E, G, H, I, J, and K are also domestic, A and G because they are local successors, the others because they are self-sponsoring. A further example of an immigrant arc is provided by the partial PN in (65) for the so-called "quantifier floating" example in (64b): (64) a. All of the men complained. b. The men all complained. (65)

all the men

complained

Here E is the immigrant arc, with B its local sponsor, and D its for­ eign predecessor. Since E is not erased, while B is, the men is the surface 1 of the clause represented. Theorem 25 shows that domestic arcs and immigrant arcs are mutually exclusive sets. Nonetheless, these two types of arc share an important property. Membership in either type requires that an arc have an overlap­ ping sponsor. The class of arcs with overlapping sponsors will be re­ ferred to as organic arcs: (66) Def. 87: Organic {A) Not (Organic (A)) . Grafts are arcs lacking overlapping sponsors. Given The PN Sponsor Condition, this means they are arcs with exclusively nonoverlapping spon­ sors. Given previous laws, there are two possible types of grafts, unisponsored and cosponsored. Replacers, for example, are cosponsored grafts (see Theorem 30 below). More generally, recalling that entrants are arcs without predecessors, there are two types of entrants: (69) a. self-sponsoring arcs b. nonself-sponsoring arcs without overlapping sponsors. (69b) is the class of grafts, thus a subset of the set of entrants (see Theorem 117 of Chapter 11). That is, the set of grafts is coextensive with the set of nonorganic entrants, while the set of self-sponsoring arcs is coextensive with the set of organic entrants. We prove the latter as follows: (70) THEOREM 26 (The Organic Entrant Theorem) Organic(A) Λ Entrant ( A) «-» Self-Sponsor ( A) . Proof. From left to right the theorem says that if an arc has an overlap­

ping sponsor and no predecessor, it is self-sponsoring. But this must be true since the only overlapping sponsor an arc can have which is not a predecessor (distinct overlapping sponsor) is itself. From right to left, the theorem says that an arc which sponsors itself has an overlapping sponsor, which is obvious, and has no predecessor, that is, distinct spon­ sor. But this is guaranteed by PN law 4, The Self-Sponsor Law. QED. Given Theorem 26 and Theorem 117, we have: (71) a. Self-Sponsoring Arcs = Organic Entrants b. Grafts = Nonorganic Entrants.

5. 5. A FUNDAMENTAL ARC TYPOLOGY

137

Arcs whose heads are pronominal forms, either "copies" or "coreferential pronouns," are (replacer) grafts of the cosponsored type. Th.e arcs labeled C in (13b) and (18) above are grafts. Similarly, in the PN for (72) in (73) C is a cosponsored graft (replacer): (72) Joe says he sings. (73)

says

Joe sings

Although C has two sponsors, neither overlaps it. It ultimately follows from the definitions of "Intrusive," "Organic," etc., and the PN laws that grafts are intrusive arcs and, more generally, the organization of arcs in these terms is: (74) a. Domestic Arcs = Organic, Nonintrusive Arcs b. Immigrant Arcs = Organic, Intrusive Arcs c. Grafts = Nonorganic, Intrusive Arcs d. (Note:

0

= Nonorganic, Nonintrusive Arcs.

(74b) is

only guaranteed by Theorem 25. See the proof of this in

Chapter 8, section 2.) Obviously then: (75) THEOREM 27 (The Basic Arc Typology Completeness Theorem) A t c (A) ··> Domestic (A) ν Immigrant (A) ν Graft (A) . Proof.

Let A' be an arc with sponsor B'. If A'= B', the definition of

"Domestic" determines that A' is domestic. If A' and B' are distinct, there are two possibilities. Either they overlap, or not. If A' and B' overlap, then A' is domestic if they are neighbors, and an immigrant if

138

5. BASIC SPONSOR AND ERASE LAWS

they are not, from the definitions. Suppose A' and B' do not overlap. There are then two possibilities. Either there is some other arc, C', which both sponsors and overlaps A', or not. If there is, then A' is domestic or an immigrant as before. If not, A' has no overlapping spon­ sor and is hence a graft. QED. Not only is every arc a member of at least one of the three basic arc categories, domestic, immigrant, or graft, but no arc is a member of more than one. These three classes are mutually disjoint. Theorem 25 shows this for domestic and immigrant arcs, and both these types are disjoint from grafts: (76) THEOREM 28 (The Graft/Organic Arc Disjointness Theorem) Grafi(A) «-» N ot (ImmigTant(A) ν Domestic (A)) . Proof, If A' is a graft then, by definition, it has no overlapping sponsor.

But the definition of "Immigrant" requires an overlapping sponsor (the foreign predecessor), and the definition of "Domestic" requires an over­ lapping sponsor (namely, the parallel sponsor). Hence, grafts are neither immigrant nor domestic arcs and the theorem is true from left to right. From right to left, the theorem simply claims that an arc which is neither an immigrant nor domestic is a graft, an immediate consequence of Theorem 27. QED. Thus, domestic arcs, immigrant arcs, and grafts are disjoint categories which together exhaust the class of arcs. However, these results do not necessarily imply that, e.g., an arc cannot have two sponsors, one over­ lapping and one not overlapping. This mistake could result from combining the exhaustiveness and disjointness of the three categories with the im­ plicit false assumption that every arc has only one sponsor. Not only has nothing been stated which prohibits an arc from having both an overlapping and a nonoverlapping sponsor, we have required that all immigrant arcs have both. We will also see that there are limited cases where domestic arcs have both overlapping and nonoverlapping sponsors (note that this is not precluded by the definition of "Domestic"), although a later law, PN

5.5. A FUNDAMENTAL ARC TYPOLOGY

139

law 18, restricts this to a single type of domestic arc. We know, however, that no such domestic arcs can be self-sponsoring, from The Self-Sponsor Law. Consequently, while in general an arc with only a single nonoverlapping sponsor is a graft, an arc with such a sponsor that also has an overlapping sponsor cannot be a graft and can be either an immigrant arc or a restricted type of domestic successor. Let us return briefly to the notions Successor and Replace discussed at length earlier in this chapter. It obviously follows from the recent dis­ cussion that: (77) THEOREM 29 (The Successor Organic Theorem) Successor (A, B) -» Organic(A) . Proof. If Successor(A', B') , then B' sponsors and overlaps A'. QED. More interestingly, one can show that all replacers are grafts: (78) THEOREM 30 (The Replacer Graft Theorem) Replace (A, B) -» Graft(A) . Proof. Assumethat Replace (A', B') but that contrary to the theorem A' is not a graft, hence is organic. The definition of "Replace" entails that A' is an entrant. Hence Theorem 26 requires that A' is selfsponsoring. But this contradicts The Self-Sponsor Law, which precludes distinct sponsors for self-sponsoring arcs, while the definition of "Re­ place" requires replacers to be cosponsored. QED. We proved above that replacers could not be logical arcs (Theorem 10). Given Theorem 30, one could show this differently as a result of the more general fact that: (79) THEOREM 31 (The Graft/Logical Arc Incompatibility Theorem) Graft(A) -» Not (Logical Arc(PC)) . Proof. Let A' be a graft. It then follows from the definition that A' has no overlapping sponsor and hence is not self-sponsoring, while all logical arcs are self-sponsoring. QED.

140

5. BASIC SPONSOR AND ERASE LAWS

We have not illustrated any unisponsored grafts. However, we claim that such exist. Chapter 10 considers in detail one type of unisponsored graft, referred to as ghost arcs. These are claimed to underlie what have been called dummy nominals in the literature. We remarked earlier that APG imposes narrow constraints on the possibilities for overlapping structural (those whose R-sign is not L or LP) arcs. The chief constraint of relevance is: (80) PN Law 13 (The Graft Overlap Law) Graft(A)

Λ

Overlap (Α, Β)

Λ

Structural(AAB) -> R-Successor(Β, A) .

(80) claims, in a distinct terminology, that if a nonself-sponsoring entrant, A, overlaps B, and A and B are structural, B must be an R-successor of A . There are then two cases. Trivially, if A = B, R-successor holds by definition. If, however, A ^ B, then A must have a successor, and B must be that successor or a successor of that succes­ sor, or, etc. PN law 13 precludes structures like the following: (81)

0

C

where A and B are structural and B is an entrant, unless A is a suc­ cessor of B or unless there is some D which is a successor of B such that A is an R-successor of D. It is irrelevant for these claims whether any of A , B , and C are neighbors. The most obvious consequence of The Graft Overlap Law is that a structural graft can never overlap a self-sponsoring structural arc. Since arcs in L-graphs must be self-sponsoring, PN law 13 determines that the heads of structural grafts are never the endpoints of L-graph arcs. Since

141

5.5. A FUNDAMENTAL ARC TYPOLOGY

replacers are grafts, this result reinforces Theorem 10, which shows that replacers are not L-graph arcs. It now follows that the heads of structural replacers cannot be node-extractable from L-graphs. We return in several places to further implications of The Graft Overlap Law, especially in Chapter 11, section 9.

5.6. A further arc typology The typology of arcs in 5.5 is based on the relation between arcs and sponsor pairs. Thedefinitionsof "Domestic," "Immigrant," and "Graft" appeal essentially only to the sponsor relation and to Neighbor and Over­ lap. There exists, however, a partially crosscutting typology of arc types which is based on the Rsigns of arcs. The first bifurcation under this typology has in effect already been given. It is that which distinguishes structural arcs from LP or L arcs. This division corresponds to the rather special roles which the grammatical relations Labels and Linear Precedence play in language. The next division divides structural arcs into two subtypes, one con­ sisting of just those whose R-sign is Cho, the other consisting of all remaining structural arcs. We refer to the latter as employed arcs: (82) Def. 89: Employed (/4) (A) ; < c i+1 > (B); < C i C lfl > (C) ; < C i > (E) ; < c i+1 > (D) . Once the coordinate C i is specified, the character of the other coordi­

nates in (6) will be determined. Moreover, one can impose a completely general law, The Self-Sponsor Coordinate Law, which identifies C i in cases like (6) as C 1 . This biconditional specifies that self-sponsoring arcs have first coordinate C 1 and, conversely, that all arcs with (first) coordinate C 1 are self-sponsoring. As (5b) shows, A, C, and E, but not B and D, are self-sponsoring. Thus, C i = C 1 and so c i+1 = C 2 : 2

2

In (7) and the other PNs in this chapter, flagging structures (e.g., preposi­ tions) are ignored. See Chapter 13 for detailed discussion of these.

6.2. DOMESTIC ARC COORDINATE DETERMINATION

153

9

'I c I

Jack

(was)seen

(by) Tina

The Self-Sponsor Coordinate Law can be formalized as follows: (8) PN Law 19 (The Self-Sponsor Coordinate Law) Self-Sponsor(A) < C j /3> (A) . Proof. By definition, all logical arcs are self-sponsoring and, hence, by

The Self-Sponsor Coordinate Law, have coordinate C1 . QED.

154

6. COORDINATE DETERMINATION

The converse of Theorem 39, < C1 β > (A) -> Logical arc (A), does not hold, given current assumptions. This is so since, as briefly mentioned in Chapter 4, there are LP arcs which are self-sponsoring C1 arcs, but which are not logical arcs, by virtue of the fact that LP is not a member of LR. However, if it ultimately turns out that such arcs really are not self-sponsoring, or do not even exist, as conjectured in Chapter 4, then the converse of Theorem 39 would hold. While we observed the desirability for B and D in (7) to have coordi­ nate C2 , no formal principle insuring this result has been presented. The key factor determining the proper coordinates for B and D is that they are both local successors. This means that B represents a linguistic state which succeeds the linguistic state represented by A. The implica­ tion is that the index of the first coordinate of an arc like B must be guaranteed to be +1 of the index of the last coordinate of its (local) predecessor, A. More generally, there is a lawful connection between the coordinate sequences of all local successor/predecessor pairs such that the first coordinate index of a local successor is necessarily +1 of the last coordinate index of its local predecessor. Since a given succes­ sor has a unique predecessor (cf. Theorem 65, The Predecessor Unique­ ness Theorem), this result is guaranteed by: (10) PN Law 20 (The Local Successor Coordinate Law) Local Successor(A, B) A < a C j >(B) -» < C j +1/3>(A) . The essential role of The Predecessor Uniqueness Theorem is made clear by PN law 20. Without predecessor uniqueness, PN law 20 would not be well defined. If PNs could contain arcs with more than one local predecessor, there would be no guarantee that in any given case, a local successor would be "assigned" a unique first coordinate by PN law 20. This point is illustrated in (11):

6.2. DOMESTIC ARC COORDINATE DETERMINATION

155

(H)

α Here A has two local predecessors, B and D, which have different final coordinates. Hence, the first coordinate of A is not uniquely determined. Later, when the coordinate "assignments" of grafts are discussed, we see that The Replacee Uniqueness Theorem plays an equally fundamental and parallel role in insuring that replacers are "assigned" unique first coordinates. There are two other important aspects of the coordinate sequences of the arcs in (7) not yet formally guaranteed: (i) that A, B , D , and E have only one coordinate, and (ii) that C has two coordinates, sharing one with A and E, the other with B and D. More generally, nothing so far precludes any given arc from having "too many" or "too few" coordinates. For example, without further restrictions, (12b) below would be, with respect to coordinates, a well-formed partial representation of (12a): (12) a. Jack sings. b.

7

Jock

sings

156

6. COORDINATE DETERMINATION

The fact that A has coordinate sequence

makes the unfound-

ed claim that (12a) involves three linguistic levels where Jack is a 1. Informally then, A has "too many" coordinates. B, on the other hand, has the right number from the viewpoint that there is exactly one linguistic level where sings is the predicate of the clause of which Jack is the 1. Before imposing the required restriction on arcs like A in (12b), we must introduce further concepts and terminology. First, it is convenient to have an expression indicating that an arc, A , has two successive coordinates,

and

In such a case, we say that A falls through

(from (13) Def. 91: A falls through (from Thus, A in (12b) has fallen through f r o m t o

and from

to

Next, it is essential to introduce within the APG framework the RG concept of

read "the c^th stratum of b " (see Perlmutter

and Postal [1977]). In a given PN, this concept stratifies each set of neighboring arcs (with tail b ) into subsets (some null) such that each subset consists of all and only the arcs with tail b which have coordinate

This concept divides any given set of arcs with tail b into

the subset o f a r c s with tail b , the subset of

arcs with tail b ,

etc. Each such subset is a stratum. Thus, there might be, in a given PN , the Cj st Stratum (99) , the c 2 nd Stratum (101), etc. In general, the c^th Stratum (b) is the set of arcs with tail b having coordinate (14) Def. 92: Let Q be an arbitrary R-graph. Then:

To illustrate, A in (12b) belongs to three strata: c 1 st Stratum (7), c 2 nd Stratum (7) , and c 3 rd Stratum (7) , while B belongs only to the CjSt Stratum(7). Thus, ( l i b ) has three strata associated with it. Related to the construct c^th Stratum (b) is the APG construct Stratal Family (b)

157

6.2. DOMESTIC ARC COORDINATE DETERMINATION

" t h e Stratal Family of b . "

The Stratal Family(b) is the set of all non-

null strata of b. For instance, the Stratal Family (7) in (12b) consists of the three nonempty strata:

Stratum (7) ,

Stratum (7) , and

Stratum (7), diagrammatically:

(15) is equivalent to:

(16)

That is, in (12b), the c 2 nd and c 3 rd Stratum (7) are identical. The formal definition is: (17) Def. 93: X Motivated (C^f^h Stratum(b)) .

+i

(19) blocks (12b). Evidently, one cannot determine whether an arc "in vacuo" has "too many" coordinates, i.e., has vacuously fallen through. The notion of vacuous fall-through is relative and can only be determined by reference to two successive strata. Returning to (7), we have so far insured: (20) < C j > (A); C 1(C); (E) -by The Self-Sponsor Coordinate Law < c 2 > (B); < C2 > (D) -by The Local Successor Coordinate Law . Further, The No Vacuous Fall-Through Law insures that there is no wellformed PN exactly like (7) with the single exception that A, B , D , and E have more coordinates. However, we have not yet provided a principle which forces C to have C2 , even though this is necessary for empirical adequacy. This is a case of nonvacuous or motivated fall-through. There are a wide range of cases where fall-through must be guaranteed, rather than blocked. The relevant law covering all such cases, The Fall-Through Law, is discussed below. 6.3. Immigrant arc coordinate determination We have provided laws governing the coordinate sequences of domestic

6.3. IMMIGRANT ARC COORDINATE DETERMINATION

159

arcs. It is also necessary to introduce laws governing the coordinate se­ quences of intrusive arcs. The first type of intrusive arc we consider is the class of immigrant arcs, the remaining set of organic arcs (see D in (5.65)). It follows from the definition of "Immigrant Arc" and The Immi­ grant Local Sponsor Law that all immigrants have two sponsors, one local and one foreign. Thus, a priori there are two arcs which could plausibly determine the first coordinate of an immigrant arc. However, one can readily rule out the foreign sponsor as a reasonable choice. In all immi­ grant cases known to us, a desirable result is achieved by guaranteeing that the index of the first coordinate of an immigrant be +1 of the index of the first coordinate of its local sponsor. More generally, we have found no cases of any sort where it is proper to allow an arc in one stratal family to affect the coordinate "assignment" of arcs in a distinct stratal family. We believe that such a situation is impossible. Coordinate determination between arcs can be restricted in all cases to neighbors, a theoretically optimal situation. The above generalization concerning the first coordinates of immigrant arcs is formally stated as follows: (21) PN Law 22 (The Immigrant Coordinate Law) Immigrant(A) Λ Local Sponsor (B, Α) Λ ( B ) -> (A) . To illustrate, (5.65) is repeated below, with appropriate coordinates added: 6

(22)

Ci CoC

-I

) believed

(to) know

French Melvin

160

6. COORDINATE DETERMINATION

In (22), B, E, H, I, J, and K are "assigned" C 1 by PN law 19. D, an immigrant arc, has first coordinate c 2 , its index being +1 of the in­ dex of the first coordinate of its local sponsor, E. A and C have first coordinate C 3 by PN law 20. The logical arcs of (22) are B, E, H, I, J, and K. In the L-graph of (22), Ted is a P-head of a 1 arc, 7 is the head of a 1 arc, and be­ lieved is a P-head of a P arc, with tail 6; and Melvin is a P-head of a 1 arc; French is a P-head of a 2 arc, and know is a P-head of a P arc, with tail 7 . In contrast, the surface arcs of (22) are A, C , G , H , J , and K. In the S-graph of (22), Ted is a P-head of a Cho arc, Melvin is a P-head of a 1 arc, 7 is the head of a Cho arc, and believed is a P-head of a P arc, all with tail 6; while French is a P-head of a 2 arc, and know is a P-head of a P arc, with tail 7. Further, D, with P-head Melvin, is neither a logical nor a surface arc. Thus, according to our analysis, the structure of Melvin is believed by Ted to know French in­ volves two clause nodes, 6 and 7. The Stratal Family (6) contains three strata:

C 1 StStratum(G)

= IB 1 E j Hl; c^nd Stratum (6) = SB, G, Hi; and

c 3 rd Stratum(6) = iA, C, G,Hi. The Stratal Family(7) contains one stratum: C 1 St Stratum(7) = {I, J,K}. 6 is transitive, i.e., has both a 1 and a 2, at

C1

and

C2

and is intransitive, i.e., has a 1 but no 2, at

C3.

In

terms of our informal interpretation, the analysis in (22) makes, inter alia, the following claims: (i) there is a clause defined by node 7, this clause involving only a single level; at this level there is a nominal correspond­ ing to Melvin which is a 1 of the clause, a nominal corresponding to French which is a 2 of the clause, and a verb corresponding to know which is a predicate of the clause defined by 7; (ii) there is a clause de­ fined by node 6 which has three levels. At the first level of this main clause, there is a verb corresponding to believed which is a predicate, a nominal corresponding to Ted which is a 1, and the clause corresponding to 7 which is a 2 of the clause defined by 6; (iii) in the second level of the main clause, the predicate is also believed, but the initial 2 is a chomeur. Melvin, which did not bear a relation in the first level, is a 2

161

6.3. IMMIGRANT ARC COORDINATE DETERMINATION

in the second level, while the initial 1, Ted, is also a 1 in the second level; finally, (iv), there is a third level corresponding to the clause 6; at this level, the complement clause is again a chomeur, Melvin is a 1, and

Ted is a chomeur. It follows that, e.g., Melvin bears three different roles in this structure. Its first status is as 1 of the complement, represented by the fact that Melvin corresponds to an entrant 1 arc in the complement. This arc has a successor 2 arc in the main clause, representing the fact that Melvin is a 2 in the second level of the main clause. Finally, that arc has a 1 arc successor, representing the fact that Melvin is a 1 in the final level of the main clause. The fact that this is the final status of

MeIvin in the sentence is indicated negatively by the fact that the main clause 1 arc headed by Melvin has no successor. (23b) below, a partial representation of (23a), provides another example involving an immigrant arc, B. (23) a. John tends to forget that. b.^

9

c, CpCs tends

(A

(to) forget

John

that

3 We regard tend as belonging to a class of verbs which take initial 2s but not Is . See Chapter 7 for further comment.

162

6. COORDINATE DETERMINATION

In (23b), C, E, G, H, and I have coordinate C 1 by PNlaw 19. B, an immigrant arc, has first coordinate C 2 by PN law 22. A and D have first coordinate indices which are +1 of the last coordinate indices of their local predecessors by PN law 20. The C 2 and C 3 coordinates of E and the C 3 coordinate of D in (23b) have not yet been formally guar­ anteed. These are both cases of motivated fall-through. Coincidentally, the first coordinate index of each immigrant arc so far exhibited has been +1 of the last coordinate index of the immigrant arc's local sponsor. Below we present the basic analysis of an example from French where the first coordinate index of an immigrant arc, B, cannot, however, be +1 of the last coordinate index of its local sponsor. (24) a. Pierre Iui a casse Ie bras. "Pierre (to) him has broken the arm" = "Pierre broke his (some­ body else's) arm." b.

(a) casse'

Gerγα Pierre

Qp Ie bras

Iui

c. Le bras Iui a ete casse par Pierre. "The arm (to) him has been broken by Pierre" = "His (somebody else's) arm was broken by Pierre." In this analysis, the PN of (24a), partially shown in (24b), involves an immigrant 3 arc, B, which is the foreign successor of a Gen arc, E.

6.3. IMMIGRANT ARC COORDINATE DETERMINATION

163

The local sponsor of B is a 2 arc, C. The most important feature of (24b) for present purposes is that A, B, C, and D all belong to the c 2 nd Stratum(IO). This aspect of (24b) is the formal representation of the informal and relatively uncontroversial view that (24a) involves a relative­ ly superficial level of structure containing a 1 corresponding to Pierre, a 3 corresponding to Iui , 4 a 2 corresponding to Ie bras, and a predicate corresponding to casse. This analysis, and in particular the key claim that Ie bras is the P-head of a 2 arc, is supported by the fact that there is a passive counterpart to (24a), (24c). In APG terms, the relevant aspects of the PN for (24c) are like (24b), except that, roughly, the 2 arc, C , is the local predecessor of a 1 arc and the 1 arc, A , is the local predecessor of a Cho arc. If the first coordinate index of B were +1 of the last coordinate in­ dex of C in (24b), it would be impossible to represent the above facts about (24a) in the current formalism. There would be no single stratum containing B and C. On the other hand, the principle that immigrant arcs have first coordinate indices that are +1 of the first coordinate in­ dices of their local sponsors achieves the desired result. We conclude that PN law 22 is the proper mechanism governing the first coordinates of immigrant arcs. Another case, involving clause union constructions, which motivates PN law 22 is discussed in Chapter 8, section 6. We are now in a position to prove a theorem of importance for coordi­ nate determination, The Immigrant Unique Local Sponsor Theorem. This has a role analogous to that of The Predecessor Uniqueness Theorem in insuring unique first coordinate "assignments" for a certain class of arcs, in this case, the class of immigrant arcs. Specifically, The Immigrant Unique Local Sponsor Theorem guarantees that an immigrant arc has at 4 One aspect of (24b) oversimplified for discursive purposes is the representa­ tion of Iui. We actually regard the form Iui as P-head of a "clitic" arc, rather than of a 3 arc as shown. In a more detailed representation, the real 3 arc would be the foreign sponsor of an arc with P-head Iui which is "inside of" the verbal element a , that is, whose tail corresponds to the tail of the arc whose head is a .

164

6. COORDINATE DETERMINATION

most one local sponsor, a necessary condition given PN law 22. The Maximal Two Sponsor Law is at the heart of this theorem, as of quite a few others, illustrating its essential function in providing a restrictive theory. (25) THEOREM 40 (The Immigrant Unique Local Sponsor Theorem) /nunigrani(A) hLocal Spo nsor(B, A)fiLocal Sponsor(C, A)

B = C.

Proof. Suppose that A' is an immigrant arc. Then, by definition A' has a foreign predecessor and, hence, can only have one other sponsor without violating The Maximal Two Sponsor Law. QED. Theorem 40, in conjunction with PN law 12, The Immigrant Local Sponsor Law, guarantees that an immigrant arc always has one and only one local sponsor, insuring that the local sponsor pair referred to in PN law 22 is invariably unique.

6.4. Grait coordinate determination At this point, we have introduced the three general APG principles

which restrict the first coordinates of all organic arcs: (i) The SelfSponsor Coordinate Law, (ii) The Local Successor Coordinate Law, and (iii) The Immigrant Coordinate Law. These laws reflect the distinction between the three disjoint types of organic arc: self-sponsoring, local successor, and immigrant arc. We now address the coordinate determination of nonorganic arcs, i.e., grafts. The set of grafts can be naturally divided into the following dis­ joint sets: (i) replacers and (ii) nonreplacers. The latter can, in turn, be split into two disjoint sets: (iii) nonreplacer ghost arcs, and (iv) nonreplacer nonghost grafts. Of these a priori possible types of grafts, we know of examples only of types (i), (ii), and (iii). We have no examples of nonreplacer, nonghost arcs. This poses something of a dilemma with respect to completely specifying first coordinates. We could hypothesize that nonreplacer, non-

6.4. GRAFT COORDINATE DETERMINATION

165

ghost arcs do not exist and impose a PN law to guarantee this result. Then, to complete the specification of first coordinates, we would only have to provide coordinate determination laws for types (i), (ii), and (iii) above. However, while we have no clear-cut examples of nonreplacer nonghost arcs, we feel that their existence is probable, especially in the domain of APG phonology, a largely unchartered territory. Hence, it would be premature to assume that this class is empty. However, not blocking them in the formalism and yet having no examples for examination make it impossible to specify the principle(s) for determining their first coordinates in a nonarbitrary way. The upshot is that at present we can­ not specify the first coordinates for every arc type formally recognized by the theory. As becomes clearer below, the actual effect of this is more limited than so far mentioned since there is a PN law specifying first coordinates for grafts lacking local sponsors (see PN law 25 below). As a consequence, the only arcs not having specified first coordinates are locally sponsored nonreplacer, nonghost arcs.

We first consider replacers (recall from The Replacer Graft Theorem that all replacers are grafts). The law needed for replacer coordinate de­ termination is parallel to The Local Successor Coordinate Law in that the first coordinate index of a replacer, in well-formed PNs, is +1 of the last coordinate index of the replacee: (26) PN Law 23 (The Replacer Coordinate Law) Replace (Α, Β) Λ (B) -» < C J +1 /3>(A). To illustrate, consider (5.12), repeated as (27), with coordinates added:

Melvm understands

166

6. COORDINATE DETERMINATION

A, B, and D have C1 by PN law 19. D has C2 by TheFall-Through Law, to be discussed below. C, which replaces B, has C2 by PN law 23. In (27), there are two strata in the Stratal Family (5): C 1 st Stratum(5) = {A,B,Di and c 2 nd Stratum(5) = {A, C, Dl. These correspond, respec­ tively, to the L-graph and S-graph representations of the clause structure of Meivin understands himself. (5.17), repeated below with coordinates added, provides another illus­ tration of The Replacer Coordinate Law. (5.17)

4

he

sings

Unlike (27), where the cosponsors of the replacer are neighbors, the spon­ sors of C, B's replacer in (5.17), have different tails. (27) and (5.17) share the property that one nominal is the head of two arcs in their re­ spective L-graphs, but not in their respective S-graphs. This does not entail an "extra" stratum for the upstairs clause. The Stratal Family (4) has only one stratum, while the Stratal Family (5) has two. This further illustrates that arcs in a stratum of one stratal family do not influence the stratal "makeup" of distinct stratal families. In the case of (5.17), the occurrence of C , via PN law 23, results in two strata for the Stratal Family (5), but has no effect on the Stratal Family (4). This result is de­ sirable since there is no evidence motivating a second stratum for the up­ stairs clause. As a final example of replacer coordinate determination, consider (5.18), repeated with some coordinates and a local sponsor for A added.

167

6.4. GRAFT COORDINATE DETERMINATION

(5.18)

j< he

Mory

loves

In (5.18), the copy arc (see Chapter 11, section 6), C, replaces B, the foreign predecessor of A. InaccordwithTheReplacerEraseLaw, C erases B. Hence, A , the foreign successor of B, does not erase B . B is self-sponsoring and so has first coordinate C1 . C1 is also B's last coordinate. Otherwisethe C1St Stratum (6) and the C2nd Stratum (6) would be identical and Cs first coordinate would be C3 , and The No Vacuous Fall-Through Law would be violated. Hence, in accord with The Replacer Coordinate Law, C has C2 as first coordinate. Analogous to The Local Successor Coordinate Law and The Immigrant Coordinate Law, arcs subject to The Replacer Coordinate Law must meet a "uniqueness condition." In any given PN, a replacer must replace only one arc. This is, however, guaranteed by Theorem 20, The Replacee Uniqueness Theorem, whose role is parallel to that of The Predecessor Uniqueness Theorem and The Immigrant Unique Local Sponsor Theorem in insuring the coordinate laws are well defined. The second graft coordinate law is PN law 24, The Ghost Coordinate Law, discussed further in Chapter 10, which specifies first coordinates for locally sponsored ghosts. This is formally parallel to PN law 22, The Immigrant Coordinate Law, in that the indices of the first coordinates of locally sponsored ghosts are +1 of the indices of the first coordinates of their sponsors:

168

6. COORDINATE DETERMINATION

(28) PN Law 24 (The Ghost Coordinate Law) Ghost(A) λ Local Sponsor (Β, Α) Α(Β) -> < cJi+>(A) . As an illustration of PN law 24 consider the German example (29a) and its partial PN, (29b)'. (29) a. Es wurde getanzt it became danced = "Unspecified danced, dancing took place"

UN

es

(wurde)getanzt

This is a so-called impersonal passive clause, a clause type discussed further in Chapter 10. C in (29b) is a ghost arc locally sponsored by A , whose first coordinate is C 1 . In accord with The Ghost Coordinate Law, the first coordinate of C is C 2 . A falls through from C1 to C 2 , moti­ vating the claim that the first coordinates of ghosts are determined by reference to first coordinates of their sponsors, just as in the case of immigrant arcs. Forif C's first coordinate were determined, e.g., by A's last coordinate, no well-formed PN could result. Under this condition, C's first coordinate would be C 3 . Ceteris paribus, this would violate The Local Successor Coordinate Law since C's local successor, B , has first coordinate C 3 . Moreover, if B's first coordinate were C 4 , in accordance with The Local Successor Coordinate Law, then A would fall through from c 2 to C 3 , in accordance with PN law 26, The Fall-Through Law, discussed below, creating the same problem again. Since ghosts are by definition unisponsored (see (10.3)), there is no question here regarding the uniqueness of the arcs determining the first coordinates of ghosts.

169

6.4. GRAFT COORDINATE DETERMINATION

So far first coordinates for replacers and locally sponsored ghosts have been formally specified. The last coordinate law to be considered is The Graft Coordinate Law, which covers all grafts without local spon­ sors and hence all foreign sponsored ghosts. This leaves open only the first coordinates of locally sponsored nonreplacer nonghost grafts. Like The Self-Sponsor Coordinate Law, The Graft Coordinate Law specifies a fixed coordinate, namely, C2 , for arcs in its domain: (30) PN Law 25 (The Graft Coordinate Law) Not((3B)(Local Sponsor(B, A))) -* (A) . PN law 25 can be stated without reference to grafts, since all organic arcs have local sponsors. The Graft Coordinate Law is illustrated by D in (5.14), repeated with coordinates added: (5.14)

Melvrn

to The F arc D in (5.14) is a graft without a local sponsor. Hence, The Graft Coordinate Law is applicable and, accordingly, has first coordinate C 2 - C ; a Marq arc immigrant (see Chapter 13 for further discussion of Marq arcs), has first coordinate C 3 , its index being +1 of the index of D, C's local sponsor. In accord with PN law 26, The Fall-Through Law, discussed below, D falls through from c 2 to c 3 . B, in contrast to D , is a replacer graft of the closure variety (see Chapter 13 for discussion of closures), and so has, via The Replacer Coordinate Law, first coordinate C 2 . Since the first coordinate of nonreplacer nonghost grafts is determined without reference to the coordinates of any other arcs, there is obviously

170

6. COORDINATE DETERMINATION

no problem regarding the unique "applicability" of PN law 25, unlike, e.g., The Replacer Coordinate Law and The Immigrant Coordinate Law. It must be guaranteed that only one of the coordinate laws "applies" to any given arc, otherwise inconsistent results could arise. For example, the importance of The Self-Sponsor Law for coordinate determination can be seen by considering what could happen without it. In such a case, there could be a self-sponsoring arc, A, which also had a local predeces­ sor, B. Then, according to The Self-Sponsor Coordinate Law, (A). But, according to The Local Successor Coordinate Law, the first coordi­ nate index of A must be +1 of the last coordinate index of B, which could be no less than C1 . Hence, the first coordinate of A would have to be C2 or greater, a contradiction. The Self-Sponsor Law insures that self-sponsoring arcs are assigned a unique first coordinate, keeping the theory consistent. The discussion illustrates that any given arc must be "assigned" a first coordinate by one and only one coordinate law. In the case of selfsponsoring arcs, this result follows from Theorems 16 and 17, The SelfSponsor Nonsuccessor Theorem and The Self-Sponsor Nonreplace Theorem, and from Theorem 28, The Graft/Organic Arc Disjointness Theorem. These theorems guarantee that a self-sponsoring arc cannot be a successor or a graft and, hence, none of the first coordinate determining laws besides The Self-Sponsor Coordinate Law could "apply" to one. In the case of The Local Successor Coordinate Law and The Immigrant Coordinate Law, The Predecessor Uniqueness Theorem (proved in Chapter 8) insures that "application" of one precludes application of the other. Theorem 28, The Graft/Organic Arc Disjointness Theorem, insures that none of the three laws determining first coordinates for organic arcs will "apply" to grafts and that none of the three laws determining first coordinate coordinates for grafts will "apply" to organic arcs. Since the graft coordinate laws are formulated in terms of disjoint sets of arcs, namely, replacers, locally sponsored ghosts, and grafts without local sponsors, "application" of one

6.4. GRAFT COORDINATE DETERMINATION

171

of these PN laws precludes "application" of the other two. It can be concluded that any given arc is "assigned" a first coordinate by at most one coordinate law. Moreover, Theorem 27, The Basic Arc Typology Theorem, determines that every arc, with the single exception of locally sponsored nonreplacer nonghost grafts, will have its first coordinate determined by one of the coordinate laws: (i) self-sponsoring domestic arcs by The Self-Sponsor Coordinate Law, (ii) nonself-sponsoring domestic arcs, i.e., local sucessors, by The Local Successor Coordinate Law, (iii) immigrant arcs by The Immigrant Coordinate Law, (iv) grafts which are replacers by The Replacer Coordinate Law, (v) locally sponsored ghosts by The Ghost Coordi­ nate Law, and (vi) grafts without local sponsors by The Graft Coordinate Law (including foreign sponsored ghosts). 6.5. The Fall-Through Law The Fall-Through Law insures that arcs have "enough" coordinates and not "too many." It "forces" an arc to fall through from Cji to Cj ifl under conditions discussed below. To illustrate, reconsider C in (7), the PN for (5a). As pointed out earlier, considerations of empirical ade­ quacy require that C have coordinate sequence < C1C2 > . Butnoformal principles yet guarantee this result. Without a principle "forcing" C to fall through from C1 to C2 , nothing would prevent there being a PN for (5a) exactly like (7), except that C would have the coordinate sequence . But this would wrongly imply that (5a), Jack was seen by Tina, is structurally ambiguous. Further, the PN for (5a), where C has coordi­ nate sequence < C1 > , would wrongly claim that there is a viable analysis of (5a) in which the nominal corresponding to Jack and the nominal corre­ sponding to ( by ) Tina co-occur in linguistic level L 2 without a predicate. Other examples of motivated fall-through include: B, G , H in (22); D and E in (23b); A, C, and D in (24b); D in (27); D in (5.17); D and E in (5.18); A and D in (29); D in (5.14); and A and D in (31b).

172

6. COORDINATE DETERMINATION

Inspection of the above PNs reveals the following aspects significant for characterizing cases of legitimate fall-through: if an arc A with tail b correctly falls through from Cj f to c^ +1 , then inevitably: (i) the Cj cf ^th Stratum (b) is motivated and (ii) there is no motivated Cj^ 1 arc with tail b which locally assassinates A . (i) simply keeps motivated fall-through consistent with The No Vacuous Fall-Through Law. Part of the import of (ii) is that foreign erasure is irrelevant to fall-through, further emphasizing the noninterference of arcs foreign to a given Stratal Family, SF (b) , in the coordinate determination of arcs in that family. Arcs foreign to a given SF (b) can influence neither first nor last coordinates of arcs in any stratum of SF (b). For example, compare the coordinate sequence of B in (32b) and (33b). In both, B has coordinate sequence < c 2 >, even though B is foreign erased only in (33b): (32) a. Max believes John was seduced by Trixie. b.

Mox

believes

John (was) seduced

(by) Trixie

(33) a. Max believes John to have been seduced by Trixie. b.

Max

believes (to)(have)(been) seduced

(by) Trixie

173

6.5. THE FALL-THROUGH LAW

The other significant aspect of (ii) above is that self-erasure also has no effect on fall-through. This is an important aspect of APG coordinate determination, since it guarantees that self-erasing arcs are always in the final strata of their stratal families (see Theorem 45 below). For example, in (34b) below, a PN fragment for (3.10a), repeated with minor changes as (34a), the self-erasing arc A is in the final stratum(62), namely, the C1St Stratum (62). This claims that (34a) is even superficially a transitive clause. (34) a. John ate.

John

UN

ate

That is, in all the strata of (34b) there are a 1 arc and a 2 arc. How­ ever, A is not a surface arc and hence does not appear in the S-graph of (10b). Consequently, under the assumption that only nodes in S-graphs are phonetically realized, the head of A can have no effect on the pho­ nology of (34a), i.e., UN is "silent." This point is made clearer by examples where there is more than one motivated stratum with the relevant tail. Consider (35a) and its partial PN (35b): (35) a. The money was donated. b

UN

the money

(was) donated

UN

174

6. COORDINATE DETERMINATION

The central aspect of (35b) for present purposes is that E has coordinate sequence , i.e., is a final stratum arc. Another example illustrating the same point is (3.11), repeated below with certain modifications: (36) a. Es deseado por todos is desired by all = "It is desired by everyone" b.

92

Cho/cg

(por) todos

el

(es) deseado

In (36b), B is the successor of A, a self-sponsoring arc, and hence has first coordinate C2 . B self-erases and so is not in the S-graph associated with (36b). However, since self-erasure has no effect on strata, unless special restrictions are imposed, B will function just like a final stratum nonerased arc. For example, inaudible el triggers singular verb agreement just like audible eso in (37). Compare the plural form (son) of the verb ser in (37b): (37) a. Eso es deseado por todos. That is desired by all = "That is desired by everyone." b. Las dos son muy simpaticas. The two are very likeable = "Both of them are very likeable." Conditions (i) and (ii) above are formalizable as: (38) PN Law 26 (The Fall-Through Law) CJ f (A) Λ (CK +1 (A)

Tail(A) = b

A

Not ((ΉΒ) (CJ

Motivated (C^ th Stratum (b)) -» 1

IFL

(B) Λ Local Assassinate(B1A)))) .

175

6.5. THE FALL-THROUGH LAW

Thisstatesthata

arc, A, falls through to a motivated Cj cfl th

stratum if and only if A is not locally assassinated by a Cj tfl arc. To see how PN law 26 prevents arcs from having too few coordinates, consider D in (36b). This P arc has the coordinate sequence . If it had fewer coordinates, i.e., if (D), PN law 26 would be vio­ lated. This is true because there is a motivated c 2 nd Stratum (92), since B is a motivated C2 arc with tail 92, and no c 2 arc locally assassi­ nates D . Similar comments hold for the following arcs: C in (7); B, G, and H in (22); D and E in (23b); A, C, and D in (24b); D in (27); D in (5.17); D and E in (5.18); A and D in (31b); and D and E in (35b). As an illustration of how PN law 26 prevents arcs from having too many coordinates, consider the structure of (39b) given in (39c): (39) a. Roger gave a ring to Joan. b. Roger gave Joan a ring. c.

Roger

Joan

a ring

gave

We analyze (39b) as similar to (39a) except that the 3 arc headed by Joaη has a 2 arc local successor, leading to a Cho arc local successor for the 2 arc headed by a ring. Hence, where (39a) is a single stratum clause, that in (39b) has additional strata. In fact, the proper stratal structure of (39c) is that in which the cir­ cled coordinates of arcs A and B are not present. If these were present, A and B would have too many coordinates. A c 3 coordinate on A would mean that (39c) is a three stratum structure. But only two strata are motivated. Hence The No Vacuous Fall-Through Law insures that an

176

6. COORDINATE DETERMINATION

arc like A cannot have a third coordinate. However, this law is not relevant to the incorrect additional (circled) coordinate on B. Forthe Cj stratum of the clause is motivated in (39c). Rather, the C2 coordi­ nate of B is precluded by The Fall-Through Law, which permits fallthrough of an arc into a Cjf stratum only if that arc has no local assassin in the Cjc stratum. But B does have a local assassin in the C2 stratum, namely, C. Of course, this discussion ignores the fact that the incorrect C2 coordinate of B in (39c) is, in effect, also blocked by PN law 20, The Local Successor Coordinate Law. For, given that law, and given the fact that the first coordinate of B's successor, C , is C2 , the last coordi­ nate of B must be C1 . Thus, there is a certain redundancy in at least some cases. This certainly raises the possibility that certain of the coordinate laws, e.g., PN law 20, might ultimately be theorems of a re­ duced set of PN laws, including The Fall-Through Law. This would yield a more elegant account of coordinate distribution than the present one. Such a potential theory deserves study.5 5 At issue is the possibility of deriving as theorems some or all of the claims made by the set of PN laws which determine the first coordinates of arcs in terms of distinct local sponsors of those arcs. The principles in question are PN laws 20, 22, 23, and 24. With the exception of the so-far unattested locally sponsored nonreplacer, nonghost grafts, these laws exhaustively determine the first coordi­ nates of all arcs with distinct local sponsors. One factor suggesting that at least some of the content of these four laws might be derivable as a theorem is that there is a generalization covering all of them. This generalization is parallel to the generalization about the coordinates of arcs related by Local Assassinate in PN law 27. The four PN laws in question determine that all of the arcs in their domain are such that the first coordinate index of the locally sponsored arc is greater than the last coordinate index of the relevant local sponsor. More precisely, if any existing locally sponsored nonreplacer, nonghost grafts are not exceptional in this regard, then the following is true:

Local Sponsor(A, B) A (Α) Λ (B) -» j > k . Assuming (i) is a truth of APG, at the moment we would be led to "derive it as a theorem from, inter alia, PN laws 20 and 22-24, given a resolution of the question about the unattested grafts mentioned above. However, the possibility exists of taking (i) as a PN law and using it, together with perhaps one or two other new laws, to derive some or all of the content of PN laws 20 and 22-24 as theorems. We leave this as a problem for future research.

177

6.5. THE FALL-THROUGH LAW

Recall from Chapter 5 that The Replacer Erase Law was formulated in the most general fashion, so The Successor Erase Law "applied" only if The Replacer Erase Law did not. Beyond maintaining internal consisten­ cy (since an arc can have only one eraser), it was mentioned that the de­ cision to complicate The Successor Erase Law rather than The Replacer Erase Law was, in part, justified by coordinate determination considera­ tions. We can now provide this justification. In (29), repeated below, B is replaced by C and is the foreign predecessor of A.

GR

Top

loves

Jack Mary

If successors were to invariably erase their predecessors, rather than only when replacers do not, in place of Erase (C, B) in (29), there would be the pair Erase (A, B). But, as observed above, foreign erasure has no effect on coordinate determination. Thus, since B would not, under the assumption of invariant successor erasure and The Unique Eraser Law, be locally assassinated, it would, in accordance with The Fall-Through Law, fall through from C1 to C2 . This would, however, be undesirable. It would "force" the c 2 nd Stratum(62) to have two 1 arcs, violating socalled stratal uniqueness (see Chapters 7 and 8). Therefore, some change in The Fall-Through Law would have to be made to keep B out of the c 2 nd Stratum (62). An ad hoc condition would have to be added

178

6. CCX)RDINATE DETERMINATION

which would not refer to local assassination, to cover cases like (29), where there is both a foreign successor and a replacer. In other words, simplifying The Successor Erase Law at the expense of The Replacer Erase Law entails an otherwise needless complication in the statement of The Fall-Through Law. Moreover, as mentioned in Chapter 5 and discussed further in Chapter 11, the present formulations of The Successor Erase Law and The Re­ placer Erase Law are independently justified. Consequently, the resultant elegant formulation of The Fall-Through Law, permitted by the above two laws, is a bonus indirectly confirming the correctness of the claim that replacers have "erasure precedence" over successors. (35b) illustrates another, distinct situation where The Fall-Through Law achieves the desired result. B , the local successor of C , locally assassinates A. As previously observed, in APG terms, arcs with P-head UN , do not locally sponsor Cho arcs in situations where arcs with so-called explicit P-heads, e.g., Mary, men, etc., would (consider D in (5b) and D in (35b) above) (see Chapter 10). We conclude that PN law 26 alone suffices to prevent erroneous fall-through in all cases, even though several principles are needed to determine first coordinates. There might seem to be a certain arbitrariness in the formulation of The Fall-Through Law in that it uses the relation Local Assassinate. One might inquire into the possibility of a more general formulation, identical to PN law 26 except that Local Assassinate is replaced by Local Erase, thereby not distinguishing self-erasure from other local erasures. However, such a formulation is not only more general, it is incoherent and leads tological inconsistencies in the case of self-erasing arcs. Consider a selferasing arc A which is in some stratum Cjc of a node b , where the ck

+1 th

stratum of b is motivated. The question is whether, under the

hypothetical version of PN law 26, A is in the c^ +1 th stratum. If A

does fall through into this stratum, a contradiction results. For there is a local eraser of A in that stratum, namely, A itself. A must then not fall through. But, in that case, A must fall through. For, if it does not,

6.5. THE FALL-THROUGH LAW

179

there is no local eraser of A in the C^ fl th stratum since A is not in it and The Unique Eraser Law prevents A from having a distinct eraser. Either alternative yields inconsistencies. Thus the choice of the relation Local Assassinate in the current formulation of The Fall-Through Law is not at all arbitrary but is based on the most basic theoretical need of maintaining consistency. Therefore, the special treatment of self-erasing arcs under this law, which sharply separates them from other locally erased arcs, is not a superficial or arbitrary decision, but a consequence of relatively deep APG assumptions. Earlier, it was observed that neither foreign erasure nor self-erasure had any effect on coordinate determination. As far as the determination of first coordinates is concerned, erasure in general is irrelevant. First

coordinates are either determined "absolutely," as in the case of The Self-Sponsor Law and The Graft Coordinate Law, or by reference to a local sponsor, as in the case of The Local Successor Coordinate Law, etc. Final coordinates, on the contrary, are always determined in a sense (see below) by The Fall-Through Law and The No Vacuous Fall-Through Law. While motivated strata are a precondition for fall-through, it is ex­ clusively the lack of local assassination which determines fall-through into motivated strata and hence which determines the final coordinates of arcs. More accurately, it can now be proved that arcs not locally assassi­ nated are final stratum arcs (are in the final strata of their stratal families). To be more precise, we introduce the following definitions, some not used until later chapters: (40) a. Def. 96: Final Coordinated^, Stratal Family(h)) *-* (ΉΑ) (Tail (b, Α) Λ Ck(A) Λ Not ((3B) (Νei ghbor (Α, Β) Λ c-(B) Λ -j > k))) . b. Def. 97: Final Coordinate (cp «-» (3b) (Final Coordinate(c^, Stratal Family (b))) . c. Def. 98: Final arc(A, Stratal Familyib )) Final arc (A) . Proof. Suppose Self-Erase (A'). Then, The Unique Eraser Law deter­ mines that A' is not locally assassinated. Hence, via Theorem 41, Final arc (A')· QED. Further, we observe the following even stronger properties of APG. Suppose that ΡΝ χ and PN y are well formed and, disregarding coordi­ nates, differ only in that one of the arcs in the arc set of PN y , A y , is foreign erased, while the correspondent of A y in the arc set of ΡΝ χ is not erased. Furthersupposethat Α χ . Then A y . That is, Α χ and A y will have identical coordinate sequences. Similarly, if ΡΝ χ and PN y differ only in that A y self-erases, then Α χ and A y will have identical coordinate sequences. We provide no proofs of these observa­ tions, because they involve the notion of isomorphism, and hence their proof would involve technical developments inappropriate in this introduc­ tory study.

6.5. THE FALL-THROUGH LAW

183

We turn to another topic which bears on the notion Stratal Family (b). So far we have guaranteed that every stratal family is (i) nonnull and (ii) finite. However, it is not insured that stratal families are continuous in the sense that if a given Stratal Family (b) has a c^th Stratum (b) and a Ck +2 th Stratum (b), then it also has a C^ fl th Stratum (b). That is, we have not insured that stratal families cannot "skip" strata. This require­ ment would be parallel to the one which requires that coordinate sequences be continuous. We could, of course, impose this as a PN law. However, this would be premature. We are confident that stratal continuity will ultimately be a theorem. Our confidence is based on the fact that the only gap in proving stratal continuity is the one induced by our current igno­ rance concerning locally sponsored nonreplacer nonghost grafts. If one assumes that either (i) locally sponsored nonreplacer nonghost grafts do not exist or (ii) they exist and the first coordinate index of such an arc is +1 of some coordinate index of its local sponsor, then stratal continuity is provable. Hence, we conjecture (47) is a theorem and prove the more restricted theorem (48), which assumes (ii) above. (47) CONJECTURED THEOREM (Stratal Continuity) c-th Stratum (b) e Stratal Family (b) Λ c^th Stratum (b) e

Stratal Family( B)

Λ

(k > i+1) -* (3j )(Cjth Stratum(b) e

Stratal Family(b) A (k > j > i)) . (48) THEOREM 46 (The Restricted Stratal Continuity Theorem) Suppose that the first coordinate index of arcs which are locally sponsored nonreplacer nonghost grafts (call these Poltergeist arcs) is +1 of some coordinate index of their local sponsors, i.e., (i) Poltergeist arc (A) A Local Sponsor (Β, Α) Λ (B) -> (Ήί) ( = (3j)(cjth Stratum(b) e Stratal Family (b) A (k > j > i)) .

184

6. COORDINATE DETERMINATION

Proof. Suppose, contrary to the theorem, that there are two successive

strata in the Stratal Family (b'), Cjth Stratum (b') and c^th Stratum (V), k > i +1, but such that: (ii) Not((!3j )(Cjth Stratum (b') e Stratal Family (b')

A

(k > j > i))) .

Clearly, the C^th Stratum (b') must be the c 3 rd Stratum (b') or greater. Further, it follows from The No Vacuous Fall-Through Law that there is some motivated arc, A', in the c^th Stratum (b') . Since A' is a moti­ vated Cj i arc, its first coordinate must be Cj c : (iii) Cj c ^C 3 , where (A / ). We show that assumption (ii) leads to a contradiction no matter what type of arc A' is. It follows from Theorem 27, The Basic Arc Typology Com­ pleteness Theorem, that A' must be either a domestic arc, an immigrant arc, or a graft. Suppose A' is a domestic arc. Then, it is either a selfsponsoring arc or a local successor. Suppose the former, then Cc 1 /3>(A') by The Self-Sponsor Coordinate Law, contradicting (iii). Suppose that A' is a local successor. Then the index of its first coordinate is +1 of the index of the last coordinate of its local predecessor, by The Local Sucessor Coordinate Law. But this contradicts (ii). Suppose A' is an immi­ grant. Then, by The Immigrant Coordinate Law, the index of its first coordinate is +1 of the index of its local sponsor's first coordinate, con­ tradicting (ii). Finally, suppose A' is a graft. Then it must be either a replacer or a nonreplacer graft. Suppose the former. Then, by The Replacer Coordinate Law, the index of its first coordinate must be +1 of the index of the last coordinate of its local sponsor, contradicting (ii). Suppose that A' is a locally sponsored ghost, then, by The Ghost Coordinate Law, the index of its first coordinate must be +1 of the index of the first coordi­ nate of its local sponsor, contradicting (ii). Suppose that A' is a graft without a local sponsor. Then, it must, via The Graft Coordinate Law, have first coordinate c 2 , contradicting (iii). Finally, suppose that A' is a Poltergeist arc. Then, from assumption (i), it follows that the first

6.5. THE FALL-THROUGH LAW

185

coordinate index of A' is +1 of the index of some coordinate of its local sponsor, contradicting (ii). QED. The reader might have assumed from the foregoing discussion that the coordinate determination laws, PN laws 19-27, suffice to insure that PNs cannot differ solely in coordinate "assignment." Informally, one might have gotten the impression that for any given sentence with postulated PN structure minus coordinates, there is only one overall coordinate "assignment" consistent with PN laws 19-27. This is not always the case, however, as the alternate structures, (49b,c) for (49a), show: (49) a. No letters were written him. b.

UN

no letters

(were) written

c.

UN

no letters

him

(were) written

(49b,c) have the same set of incomplete arcs. They differ in that (49b) has two motivated strata, while (49c) has three. The reader can verify that (49b,c) are both consistent with PN laws 19-27. Ignoring the P arc,

186

6. COORDINATE DETERMINATION

(49b), however, does not involve fall-through. Informally, (49b) involves "simultaneous" sponsoring of local successors, namely, Sponsor(B, A) and Sponsor(D j C), while in (49c) the sponsorship of C by D is "de­ layed" to C 2 . It is our conclusion that in certain instances, such as the one above, no choice between the two alternatives can be made at the level of APG universal grammar. That is, the choice between the two must be determined by the grammars of individual languages. (See Chapter 8, section 4 for further discussion of this topic, which we call "Stratal Compactness.") At this point, we have developed the "skeleton" of the theoretical apparatus needed to represent the grammatical structures found in natural languages. That is, we have introduced the core of the APG theoretical framework. We have, in addition, ruled out many logically possible struc­ tures (PNs), thereby claimed to be empirically impossible in real lan­ guages. In particular, in this chapter, the PN laws governing coordinate determination have been formally specified and illustrated. These PN laws are part of the "core theoretical apparatus" of APG since they are basic to a formal explication of the fundamental pretheoretical notion of linguistic level. Of course, a vast number of additional constraints must be imposed on PNs to arrive at an empirically adequate theory. The following chapters introduce many further laws. However, at this stage in the development of APG, one can, obviously, state only a small percent­ age of the PN laws which must ultimately be assumed to exist. Before leaving the subject of coordinate determination, we should restress that the set of coordinates is quite small. We conjecture that when APG is more highly developed, it will be possible to prove (i) that there is an upper bound on the number of strata in an arbitrary stratal family and that (ii) this upper bound is small, i.e., on the order of ten or less. We would not be surprised if it turned out to be as low as five or six.

6. 6 . An alternative view of coordinates In the present version of APG, each arc contains a coordinate se­ quence. In general, such sequences contain more than one member. As

6.6. AN ALTERNATIVE VIEW OF COORDINATES

187

specified in this chapter, an arc has more than one coordinate if and only if it falls through into one or more motivated strata. The conditions gov­ erning such fall-through are specified in The Fall-Through Law. There are logically possible alternatives to the current theory which would restrict each arc to a single coordinate. Hence, in terms of the definitions in (40) above, each arc would have the same first and final coordinates. A natural alternative of this type would provide (50b) as the PN fragment for the structure represented as (50a) in the current framework:

6 b.

7 5

Let us refer to frameworks like that which yield (50b) as unicoordinate models. In such an approach, no arc ever falls through. Hence, in cases like (50), to guarantee that a node like 6 heads an arc in the second stra­ tum of node 5, it is necessary for arc G to have a local successor, and, moreover, one which is its facsimile, that is, which has the same R-sign. Since this is inconsistent with PN law 5, The Local Successor Distinct R-sign Law, unicoordinate models must dispense with that law. Clearly, unicoordinate approaches to APG will also not be able to in­ corporate the current Fall-Through Law, They will, however, need an

188

6. COORDINATE DETERMINATION

analogue of this, to guarantee that facsimile local successor pairs like Local Successor(H, G) in (50b) are invariably present. Obviously, many other revisions would necessarily be induced by any switch from the cur­ rent coordinate sequence approach to a unicoordinate model. It is not clear just how different unicoordinate models are from the coordinate sequence approach adopted in this volume. We do not know to what extent a precisely and extensively developed unicoordinate model would yield distinct empirical predictions, distinct theorems, etc. Hence it is not easy at this stage to answer the natural question: is the proper form of APG based on arcs with nonunary coordinate sequences, or on those with uniformly single coordinate arcs? While we have not studied this question in detail, and regard it as to a certain extent open, the choice made in the current work is not complete­ ly arbitrary. There are good initial reasons for preferring the coordinate sequence approach, namely, it yields PNs which are conceptually simpler with no known loss of descriptive power. For instance, the coordinate sequence structure in (50a) involves three sponsor pairs, one erase pair, three arcs, four coordinates, and three R-signs. The unicoordinate struc­ ture in (50b) involves four sponsor pairs, two erase pairs, four arcs, four coordinates, and three R-signs. As the complexity of the linguistic struc­ tures to be represented rises, the relative "numerical" advantages of a coordinate sequence approach become more pronounced. We conclude that unless some serious theoretical or empirical motiva­ tions can be found for preferring unicoordinate models, the criterion of conceptual simplicity of descriptions supports the choice made here to base APG theory on arcs whose coordinate sequences are not necessarily unary.

CHAPTER 7 FOCUS ON CLAUSE STRUCTURE 7.1. Comments The bulk of work in APG, as in stage 1 and stage 2 RG, has involved the study of clause structure, e.g., such topics as passivization, "raising,' "reflexivization," impersonal constructions, etc. Despite this, we have developed APG in extremely general terms, providing, we hope, the basic apparatus for the description of all aspects of grammatical structure. How­ ever, the overwhelming body of empirical research bearing on APG remains in the area of clause structure and most of the empirical results obtained lie in this domain. Thus, certain assumptions which we have framed in quite general terms are largely motivated by work in a relatively narrow (if huge) domain, and may require modification on the basis of work in, e.g., tense systems, the internal structure of nominals, complex verbal morpholo­ gies, word derivation, etc. At this point then, it is relevant to slightly re­ orient the discussion toward the more particular domain of clause structure on which APG work and previous RG work has concentrated. The present chapter therefore surveys some general features of clause structure in APG terms, proposes various laws characterizing clauses, and introduces further concepts. In the following two chapters we concentrate on the important concept of the chomeur relation developed in RG and its formalization in APG terms. This distinctive contribution of RG is basic to the APG conception of clause structure.

7.2. Grammatical categories arid constituents The notions of grammatical category and constituent have played a role in all linguistic frameworks and have been especially brought to

190

7. FOCUS ON CLAUSE STRUCTURE

prominence in transformational work. They play a much more marginal role in APG. As seen in Chapter 2, APG recognizes a class of terminal nodes, GNo , whose members represent grammatical categories. Wenowconsider how these elements relate to constituency and how they are used to assign nonterminal nodes to grammatical categories. What is usually referred to as a constituent is reconstructable in APG terms as an R-graph. Every R-graph has a point, a unique root which R-governs every node forming an arc in the set. Of course, in general, the R-graphs defining constituents are proper subsets of more inclusive R-graphs. That is, in almost all cases, the R-graphs defining constituents are not the arc sets of PNs, but proper subsets of such arc sets. This account of constituency is inadequate in an obvious respect. It ignores the need to specify that an R-graph, O, whose point is node a reconstructs the constituent corresponding to a only if Q is the maximal R-graph with a as point in some fixed set of arcs. This notion is formalizable in terms of set inclusion, given that R-graphs are sets of arcs. Formally, we introduce constituency as a ternary relation between an R-graph, its point, and some set of arcs containing that R-graph: (1) Def. 108: Let X be an arbitrary set of arcs. Then: Constituent (Q,a,X) "Q is a constituent of X corresponding to node a"

«-» R-graph(Q)

A

QC X Λ Point(a, Q) Λ ((VQ1)(R-graph(Q1) Λ

Q 1 C X Λ Point (a, Q 1 ) -» Q 1 C Q)) .

The complex last conjunct of the defining expression of the notion is the maximalness condition. Given (1), we can speak of constituents rigorously, but we still have no formal way of categorizing constituents, e.g., of speaking, as is standard, of nominal constituents, clausal constituents, verbal constituents, etc. Evidently at issue is a characterization of the point of the R-graph defining the constituent. A nominal constituent is simply one whose (necessarily nonterminal) root(point) is a nominal node, etc. The question is how to characterize notions like nominal node, clause node, etc. Here there seem to be two logical possibilities.

7.2. GRAMMATICAL CATEGORIES AND CONSTITUENTS

191

Most interestingly, one could attempt to formulate definitions of these notions which would pick out the class of nominal nodes on the basis of independently existing properties of the R-graphs of which they are points. Unfortunately, for the categories which actually seem relevant for natural languages, we do not see how to do this. Moreover, we offer some con­ siderations below (in the discussion of coordinate structures) which sug­ gest that it cannot be done. There appear to be, for example, no nondisjunctive necessary and sufficient conditions for being a nominal node, a clause node, etc. Therefore, we are driven to the other alternative, simi­ lar to that adopted in other frameworks, like TG. We characterize nominal nodes, clause nodes, etc., in part (see below) by recognizing special sym­ bols like Nom, Cl, and other GNo members, and associating these sym­ bols with the nodes to be assigned to categories. A nonterminal node a will be assigned to the grammatical category X if and only if a is the tail of a grammatical termination whose head is X. Since we know from The Labeling Condition part of the definition of "R-graph" that all terminations are L arcs, characterizing a node a as a member of the category X will require an arc of the form: (2)

a ( NTNo

X e GNo Therefore, when a is the point of a constituent Q , Q is an X constitu­ ent. One can formally define a variety of constituent types of this sort simultaneously by making use of the concept Node Label from Chapter 2: (3) Def. 109: Z Constituent (Q) *-* Constituent (Q, a, Χ) Λ Node Label (a, Z)) λ Z e GNo .

Hence, for Z = Cl , Nom , V, etc., definition (3) defines respectively Cl Constituent, Nom Constituent, V Constituent, etc., which are traditionally,

192

7. FOCUS ON CLAUSE STRUCTURE

and here also, referred to as clauses, nominals, verbs, etc. The defini­ tions in (1) and (3) pick out a certain class of R-graphs as clauses, verbs, etc. But equivalently they also, in effect, characterize certain classes of nodes, namely, the points of these R-graphs, as clausal nodes, nominal nodes, etc. We can make this explicit: (4) Def. 110: Z Node (a) Entrant(A) . *

PN law 32 has many consequences. It claims, for instance, that category assignment is independent of grammatical phenomena like passivization, etc. A node which heads a 2 arc cannot be labeled one way if that 2 arc fails to have a 1 arc local successor and another way if it does have such. That is, passivization cannot "change" the category of the passivized nominal, etc. Similarly, (31) claims that it is impossible for a nominal which would otherwise be masculine to be feminine just in case it heads some successor arc. Thus, like passivization, raising, topicalization, and other phenomena which involve successor arcs (see below) can have no effects on grammatical categories, given PN law 32. There is an obvious analogue of PN law 32 for phonological terminations: (32) PN Law 33 (The Phonological Termination Law) Sponsor (A, B)

A

Phonological Termination(B) -> Entrant(A) .

PN law 33 claims that the choice of phonological node is in all cases in­ dependent of successor arcs. While we have not studied the domain covered by (32) in detail, we know of no evidence against it, and hence tentatively impose it.

206

7. FOCUS ON CLAUSE STRUCTURE

One might raise the question of the principle parallel to PN laws 32 and 33 involving logical terminations. However, there is no relevant PN law in this domain since one can prove from independent assumptions not only that all logical termination sponsors are entrants, but that these arcs are self-sponsoring: (33) THEOREM 47 (The Logical Termination Self-Sponsor Theorem) Logical Termination (A) -> Self-Sponsor (A) . Proof. It follows from The L-graph Completeness Condition that every logical termination in the arc set of a PN is in the L-graph of that PN. And L-graphs are logical arc sets, with membership in the latter deter­ mined by self-sponsorship. QED. But obviously: (34) THEOREM 48 (The Self-Sponsor Entrant Theorem) Sel f-Sponsor (A) -» Entrant ( A) . Proof. Immediate from Theorem 16(5.32) and the definition of "Entrant." QED. Consequently, the current theory determines that: (35) THEOREM 49 (The Termination Theorem) Sponsor( Α, Β) Λ Termination(B) -> Entrant(A) . Proof. Immediate from PN laws 32 and 33 and Theorems 47 and 48. QED. There is one final principle determining grammatical category labeling which we wish to discuss. This involves coordinate structures. Coordinate structures involve, in APG terms, arcs with the R-sign Con. For example, a simplified representation for the coordinate clause in (36) would be (37) (note that this ignores most sponsor relations): (36) Ted sang and Melvin danced.

207

7.3. DETERMINATION OF NODE-LABELING

55

Ted

sang

Melvin

danced

Coordinate structures involve a host of problems, for instance, that which has been discussed under the rubric "conjunction reduction" in transformational linguistics. There are also questions, raised by McCawley (1972) as to whether coordinate structures actually involve a defining predicate, and many others. We do not enter into these questions here, since we have not had the chance to study this area in APG terms. Previous laws guarantee that arcs G and J in (37) exist, sponsored by E and I respectively. Ofcurrentinterestis B. Theexistenceof B is indicative, we claim, of a regularity. Namely, the heads and tails of Con arcs must be labeled with the same Major category. That is, coordi­ nate clauses involve conjunctions of clauses, coordinate nominals involve conjunctions of nominals, etc. We can express this formally as follows: (38) PN Law 34 (The Con Arc Endpoint Label Identity Law) Con arc (A) -» (Head Label (Major x , A) (3A) (Con arc (A) ATail (a, A)) . Simultaneously, we define the related though distinct concept Conjunctive for the heads of Con arcs: (41) Def. 123: Conjunctive (a) «—» (ΉΑ) (Con arc (A) A Head (a, A)) . Hence, in (37), 55 is coordinate while 10 and 20 are conjunctive. We can now speak of conjunctive constituents, whose points are conjunctive, and coordinate constituents, whose points are coordinate. Basic constituents

Q

This vague idea is made more precise by PN law 53 in the text below. This requires every PN to "contain" a basic clause like that corresponding to nodes 10 and 20, there being no parallel law with respect to conjoined clauses.

210

7. FOCUS ON CLAUSE STRUCTURE

will then be defined so that their points are not coordinate, it being irrel­ evant whether they are conjunctive or not. The second property we claim relevant to defining basic constituents involves picking out those constituents whose points are the tails of selfsponsoring arcs. We refer to such nodes as Inherent. (42) Def. 124: Inherent(a) «—> (3A) (Self-Sponsor(A) λ Tail (a, A)) . We may now speak of inherent constituents, whose points are inherent nodes. Hence we can refer to inherent clauses, etc. The motivation for distinguishing inherent nodes can be seen in cases like: (43) a. What will Sally say? b. I donated to the United Anarchist Appeal all of the funds I inherited. In (43a), we assume that the first word is an element of a constituent, X , distinct from that corresponding to the italicized forms. In our terms, X is necessarily a clause. 9 However, it is not a clause we would wish to characterize as a basic clause, since it contains no predicate, etc. Our claim is that the overall constituent corresponding to the entire surface clause in (43a) is not inherent, that is, none of its arcs are self-sponsoring. Hence, by picking out only inherent constituents to be basic clauses, we will, as desired, exclude whole surface sentences like (43a), but include the subclauses they contain. Similarly, in (43b), we regard the final nomi­ nal as a constituent of an overall constituent, which is also presumably a clause, but not one we wish to consider a basic clause. Again, this re­ sult is apparently achievable by reference to inherent constituents, since we assume that the overall constituent in (43b) also involves no self-

9 This follows since X is a surface sentence and hence the point of X is a quasi-root in the sense of Chapter 4. Hence, (4.29d), The S-graph Quasi-Root Condition, requires that the point of X be labeled Cl .

211

7.3. DETERMINATION OF NODE-LABELING

sponsoring arcs. In section 6 below and in Chapter 13, we suggest that forms like what in (43a) and all of the funds which I inherited in (43b) both head Overlay immigrant arcs. We are now ready to define the notion Basic Constituent. We will take these to be the intersection of inherent constituents with noncoordinate constituents.10 (44) Def. 125: Basic Z Constituent (Q) Z Constituent(Q)

Λ

Inherent (Point (Q)) Λ Not (Coordinate (Point (Q))) . Hence, for Z = Cl, Norn, V, etc., (44) defines such notions as Basic Cl Constituent, Basic Nom Constituent, Basic V Constituent, etc., which we will refer to as "basic clauses," "basic nominals," "basic verbs," etc. Basic clauses will be a major focus of attention in what follows. To conclude this section, observe that we have not required that every member of NTNo be node-labeled with some member of GNo . We have left open and continue to leave open the possibility that there could be constituents not assigned to any particular category.

It is easy enough to state a law which would require such labeling of every nonterminal node. But it is quite a different matter to decide what category is appropriate for each constituent and what laws assign that category, as well as what arcs sponsor the terminations of which the rele­ vant category labels are the heads.

7.4. Some properties of basic clauses: predicates Having briefly sketched our approach to constituents and grammatical categories and having formally picked out the class of basic clauses which are the focus of attention, we can begin to specify what we take to be the characteristic properties of these entities. ^Evidently this is redundant if all coordinate nodes are noninherent. But since there is ultimately presumably a law saying that the only structural arcs whose tails can be coordinate nodes are Con arcs, this could only be true if no Con arcs are self-sponsoring. This seems too doubtful to lean any aspect of a theory on at this stage.

212

7. FOCUS ON CLAUSE STRUCTURE

A notion of some importance in discussing basic clauses is that of a P arc which is self-sponsoring. For convenience we introduce a single term for this: (45) Def. 126: Primary(A) 1 .

Therefore, from (i) and the fact that coordinate sequences are continuous, we have: (iii)

c k-i( A ')

·

From The Neighboring P Arc Erase Law and the contrary of the consequent we know that: (iv) Local Assassinate (B', A') . 16 The erasure mandated by PN law 40 is of a relatively rare and highly re­ stricted type, that is, zeroing of an arc by a nonsponsor. Chapter 9 imposes strict constraints on this kind of assassination, for the class of Nominal arcs. See PN laws 76-78.

220

7. FOCUS ON CLAUSE STRUCTURE

But from (iv), the assumption that Cj c (B y ) and The Fall-Through Law, it follows that: (v) Not(c k (A'))· This contradicts the original assumption that A' and B' are both Cj i arcs. QED. Thus, it is guaranteed that a basic clause either has a single P arc, which is a primary, or two P arcs, one of which is primary, and the other of which shares no coordinates with the primary. Another consequence of current assumptions about clauses is that every basic clause "contains" a verb. Moie precisely: (63) THEOREM 53 (The Basic Clause Verb Existence Theorem) Basic Cl Constituent (Q) -» (3A) (Tail (A) = Point(Q ) A H e a d Label (V, A)) . Proof. Let Q' be a basic Cl constituent. The Basic Clause Predication Law entails that there is a P arc, call it A', with the point of Q' as tail, and that A' is self-sponsoring, hence an entrant. Thus it follows from The P Arc Head Label Law that the head of A' is labeled V. QED. Notice that our analysis of predicate nominal clauses is not incompatible with this theorem. In our analysis of such clauses there is a V node (entirely independent of the auxiliaries found in some languages), namely, the node heading the primary arc necessarily erased via The Neighboring P Arc Erase Law. Theorem 53 guarantees that every basic clause node is the tail of an arc whose head is labeled V . It does not, however, preclude the exist­ ence of more than one such arc. It might be thought that this is ruled out since recent PN laws allow a clause only one verbal predicate. However, multiple verbs are obviously not ruled out as long as at most one of these is the head of a P arc, the others being heads of nonP arcs. Nothing pre­ cludes a situation of the form:

7.4. BASIC CLAUSES: PREDICATES

221

55

IO'

20

V This, however, is no weakness since such situations exist, e.g., in socalled clause union constructions (see Chapter 8, section 6). These are illustrated by a French example such as (65a), whose structure is given in (65b): (65) a. Pierre a fait partir Marie. Pierre has made leave Marie= "Pierre made Marie leave." b.

(a)foit partir Marie

V As indicated, both fait and partir are claimed to correspond to V nodes which are the heads of arcs whose common tail is the point of (65a) as a whole. However, fait is on an arc whose R-sign is P, while partir is on an arc whose R-sign is U , the R-sign particular to arcs relevant to clause union constructions. Here both B and C have V nodes for heads, but the U arc C is an immigrant successor of the complement P arc. Only B is a primary of the main clause. Thus, (65b) offers a model of (64) and indicates that no law should rule out such situations in general.

222

7. FOCUS ON CLAUSE STRUCTURE

Basic clauses must "contain" at least one verb, but can "contain" others as well. However, only one of these can be the head of a P arc whose tail is the point of the basic clause constituent. While a basic clause node can govern more than one verb node, there are no doubt strict constraints on this possibility, and in general, strict constraints on the distribution of V nodes in PNs. Unfortunately, it is not clear to us how to best impose further constraints. One limitation which seems valid is that the possibility of multiple verbs is limited to situations like that in (65b), where one verb is the head of a primary, all others the heads of immigrant arcs. Further, it is clearly necessary to limit the class of arcs whose heads can be V nodes. In (65b), V nodes occur as the heads of a U arc and a P arc. It seems clear from cases like: (66) a. The fiend shot and knifed his victim. b. Which nurse did the fiend shoot and knife? that there are coordinate V nodes and hence that V nodes occur as the heads of Con arcs. But outside of P arcs, U arcs, and Con arcs, we know of no structural arcs clearly headed by V nodes. Hence there is a fertile field here for further PN laws. Clearly, there are a host of arcs, including all Central arcs and possibly all Nominal arcs, 17 whose heads cannot be V nodes. It might be thought provable that, e.g., Central arc heads cannot be V nodes, by appeal to The Central Arc Head Label Law and The Major Cate­ gory Exclusiveness Law. For the former says that heads of certain Cen­ tral arcs not labeled Cl are labeled Nom, and the latter says that Nom and V are incompatible labels. However, no such theorem is provable in general since all of the labeling laws are restricted to claims about entrant arcs. Thus all one can prove is that no entrant Central arc can have a V node for a head. This in itself does not preclude the nonetheless 17 The question here is whether there are Overlay arcs headed by V nodes, e.g., Top arcs which are successors of P arcs headed by V nodes. See the text below»

7.4. BASIC CLAUSES: PREDICATES

223

evidently impossible situation where, e.g., an entrant P arc has a 2 arc or 3 arc successor. We can take steps toward eliminating some such situations by noting that we have also not so far guaranteed any "preservation" of P arcs in the following sense. The Basic Clause Predication Law guarantees that every basic clause has an initial stratum P arc. But nothing guarantees that a basic clause has a P arc in other strata, in particular, in its final stratum. We thus propose: (67) PN Law 41 (The Basic Clause P Arc Continuity Law) Cjth Stratum (b) e Stratal Family (b) λ (Point (b, Q) λ Basic Cl Constituent(Q) -» (3A)(P βκ:(Α)Λ Aec^th Stratum(b)) . According to (67), every nonempty stratum of a basic clause constituent root contains a P arc. This does not require that the P arc in question be a surface arc. The latter claim would clearly be falsified, inter alia, by the second clauses in examples like (68a): (68) a. Melvin likes white bread and Sally whole, wheat. b. Joe wants to dance but Mary doesn't want to. But in such "gapping" cases one is dealing with foreign erasure of the second clause P arc by the first clause P arc. And, as shown in Chapter 6 (see Theorem 44), foreign erasure provably has no effects on the coordi­ nates of the erased arc, which is necessarily a final stratum arc. A simi­ lar point would hold for so-called VP deletion cases like (68b). Here also we would claim that the final clause (the complement of the want clause) has a foreign-erased P arc and thus a final stratum P arc, the example being irrelevant to PN law 41. Interestingly, given The Basic Clause P Arc Continuity Law, one can prove that P arcs cannot have local successors: (69) THEOREM 54 (The P Arc No Local Successor Theorem) P arc (A) -> N oi((3B) (Local Successor (B, A))) .

224

7. FOCUS ON CLAUSE STRUCTURE

Proof. Let A' be a P arc. There are two cases to consider:

Case (a) A' is a primary. If so, then either there is a distinct neighbor­ ing P arc, or not. If not, then by The Basic Clause P Arc Continuity Law, A' is a final stratum arc, and hence, by The Fall-Through Law, not local­ ly assassinated. But if A' is not locally assassinated, it can have no local successor, for arcs with local successors are erased either by these successors or by a replacer (see Theorem 8). Hence, if A' is a primary, it has no local successor. Case(b) A' is not a primary. The Nonprimary P Arc Law says that A' is the neighbor of a primary, say B', and The Neighboring P Arc Erase Law says that A' erases B'. B' is then not a final stratum arc. But The Basic Clause P Arc Continuity Law requires there to be a final stra­ tum P arc. Sincethiscannotbe B', it must be A' or an arc distinct from both A' and B'. ButTheUniquePrimaryLawandTheMaximal Two P Arc Law guarantee that there can be no third P arc distinct from both A' and B'. Consequently, A' must be a final stratum arc. But The Fall-Through Law stipulates that this can only be the case if A' has no local successor. For if it has such, it will be locally erased either by that successor or a replacer. QED. Theorem 54 in no way precludes foreign successors for P arcs, and neither does anything else we have stipulated. This is important, for, of course, in structures like (65b) we posit U arc foreign successors for P arcs (C is the U arc foreign successor of P arc G in (65b)). Thus, what we ultimately require are constraints on the class of arcs which can be foreign successors of P arcs. This class is very small, and could, conceivably be limited to U arcs or one or two other types. 18 But we do not feel capable of specifying this area in detail at the moment. 18 A major question here, on the assumption that many nominals involve "nominalized" clauses, and that this requires P arc successors, is what kind(s) of arcs are the successors of P arcs in such cases. Possibly a unique type of arc would be relevant, and it is not out of the question that one could ultimately identify this arc type with U arcs, restricted in this volume to the description of clause union constructions.

7.4. BASIC CLAUSES: PREDICATES

225

To conclude the current discussion of P arcs and primaries, we want to close an important gap in our discussion. Pretheoretically, we would like the heads of primary arcs to correspond to logical predicates, so that the existence of primaries in L-graphs will serve to define L-graphs which are coherent logical structures. So faf, however, nothing guarantees this. We can accomplish this by requiring that the head of every primary be labeled with some logical node: (70) PN Law 42 (The Primary Logical Node Law) Primary(A) -» (ΉΒ) (Logical Termination(B)A Branch (B, A)) . As informally observed in Chapter 4, section 2, PN law 42 in connection with other assumptions guarantees that every L-graph contains a logical node. However, possibly (70) is too strong. In particular, in the case of some auxiliary verbs, it may be incorrect to head label primary arcs with logical nodes. 19 7.5. Some properties of basic clauses'. Nominals We said earlier that the bulk of work in RG and APG was limited to the study of basic clauses. It would be even more accurate to say that most such work has concentrated on the properties of the nominals of clauses, on the relations such nominals bear to basic clauses and to each other. In this section, we consider what we take to be some basic features of the nominal elements of basic clauses. Informally, the self-sponsoring arcs of basic clauses correspond to representations of propositional structures in L-graphs. PN law 42 guar­ antees that any such structure will involve a logical node. But a logical predicate will be incoherent unless it has one or more arguments. Corre-

19 The question is whether those auxiliary verbs like the passive be and tense support do in English correspond to semantic elements. If not, then in our terms, there are P arcs whose heads are not the tails of logical arcs. We leave this question, like many others relating to the treatment of auxiliaries, open.

226

7. FOCUS ON CLAUSE STRUCTURE

spondingly, we claim that a basic clause cannot exist unless it has one or more nominal components, some of which necessarily correspond to arguments in the L-graph. In discussing nominals, we make extensive use of the classes of arcs defined by the classes of R-signs in (6) above, that is, Nominal arcs, Core arcs, Term arcs, Oblique arcs, etc. In addi­ tion, we will, as in earlier chapters, sometimes informally use terms like a term, a 1, a 2, a Ioc, etc., to refer to a node which is respectively head of a Term arc, a 1 arc, a 2 arc, a Loc arc, etc. Recall that these cate­ gories are not necessarily exclusive. A single nominal can be, and often is, both a 1 and a 2 , both a Ioc and a 1, etc. Our framework now permits a more precise range of claims about the role of nominals in basic clauses, as follows: (71) a. Every basic Cl node governs a Nom node. b. Every basic Cl node is the tail of a Term arc. c. Every basic Cl node is the tail of a Nuclear Term arc. d. Every basic Cl node is the tail of a self-sponsoring Term arc. e. Every basic Cl node is the tail of a self-sponsoring Nuclear Term arc. Each principle in (71) entails all the preceding statements in (71). We believe that all of these claims are correct, and can impose them all by specifying the content of (71e) as a PN law. We have introduced (71a-e) in this manner to stress both their logical independence and their logical connections. (72) PN Law 43 (The Self-Sponsoring Nuclear Term Arc Law) Basic Cl Constituent (Q) Λ Point (a, Q) -» (3A) (Nuclear Term arc (A)

Λ

Tail (a, Α) Λ Self-Sponsor(A)) . Given PN law 43, we have imposed what we believe to be the two essen­ tial conditions on basic clauses. Each such clause must involve a selfsponsoring P arc (a primary) and a self-sponsoring Nuclear Term arc.

7.5. BASIC CLAUSES: NOMINALS

227

Therefore, the first stratum of every basic clause point is the C 1 stratum, and that stratum contains at least a P arc and either (or both) a 1 arc and a 2 arc. There is a rich tradition which suggests, in effect, that The SelfSponsoring Nuclear Term Arc Law be strengthened to require each basic clause node to govern not just a nuclear term, but a 1. This would claim that every basic clause has a self-sponsoring 1 arc. This view is pretty much coextensive with the doctrine that all intransitive clauses involve initial stratum 1 arcs. However, we do not believe this. Rather, in accord with a body of RG work, 20 we believe it necessary to analyze some intransitive clauses as involving only initial stratum 2 arcs.

In other words, traditional grammar recognizes in effect two types of Is, a 1 contrasting (at a level) with a 2, and a 1 not so contrasting. We agree with this and in addition recognize two types of 2, a 2 con­ trasting at a level with a 1 and a 2 not so contrasting. Traditionally, Is contrasting with 2s are called transitive Is , or, in many cases, ergative Is, while intransitive Is are also called absolutive Is. This terminolo­

gy will be formally introduced below and is quite useful in rule statements. It is also useful to distinguish transitive 2s , which we call accusative 2s , from intransitive 2s , which we will call unaccusative 2s . Our major

novel claim is thus that there are unaccusative 2s , where traditional grammar for the most part recognizes only transitive 2s . While we do not require that a basic clause necessarily involves a self-sponsoring 1 arc, there are constraints on basic clauses which re­

quire the presence of 1 arcs. The weakest constraint in this area would say that every basic Cl node is the tail of a 1 arc. However, we will not specify this as a PN law because, while confident that it is true, we sus­ pect it is merely a special case of a stronger constraint. This requires

20 See Perlmutter and Postal (to appear b), Perlmutter (1978), and Postal (to appear b).

228

7. FOCUS ON CLAUSE STRUCTURE

every basic clause to "contain" a 1 arc as a member of the last stratum of that clause. In other words, this claims that every basic clause has a final stratum I arc. (73) PN Law 44 (The Final 1 Arc Law) Basic Cl Constituent(Q)A Point(b,Q) -> (3A)(AfFinal Stratum(b)A 1 arc (A)) . In requiring that a basic clause have a final stratum 1 arc, PN law 44 does not require that the final 1 arc be a surface arc. Thus (73) is not immediately falsified by italicized basic clauses like those in: (74) a. Eat your meat. b. Joe picked up his fork and then ate his meat. c. Why not eat your meat. Such clauses lack, to be sure, surface 1 arcs. But this is irrelevant to The Final 1 Arc Law. Such examples would only become relevant to this constraint if it could be argued that they not only lack surface 1 arcs, but also final stratum 1 arcs. But we see no reason at all to assume this in these or any other cases. In (74a,c) there are, we suggest, probably self-erasing 1 arcs. If so, then Theorem 45 of Chapter 6 demonstrates that these clauses contain final stratum 1 arcs and are hence consistent with PN law 44. On the other hand, it is conceivable that the 1 arcs in (74a) are foreign erased, by overlapping arcs, say 3 arcs of certain structures which represent the addressee of the sentence. 21 But foreign-erased arcs are also provably final stratum arcs (see Theorem 44). Similarly, in (74b), the 1 arc of the 21

We are considering the possibility that e.g., (74a) might have a structure in­ formally representable something like: (i) I order to you that you eat your meat. Here the italicized form represents the head of a 3 arc. The proposal would be that the vanished 1 arc in the S-graph clause does not self-erase but is foreign erased by the 3 arc representing the indirect object relation of the order clause. Something like this has been suggested in transformational terms by, e.g., McCawley (1968b: 155-57).

7.5. BASIC CLAUSES: NOMINALS

229

italicized clause is definitely foreign erased, by the 1 arc of the main clause, and thus is a final stratum arc. Analogous remarks hold for those many languages in which, e.g., weak definite pronominals can or must be deleted. For example, in Spanish, one finds: (75) estoy cansado am-I

tired

= "I am tired."

Such clauses also lack surface 1 arcs because, in our terms, the 1 arc has self-erased. But there is no reason to assume they lack final stratum 1 arcs. On the contrary, since the verb agrees with its 1, and it is a plausible hypothesis that this agreement involves reference to the heads of final stratum 1 arcs, this supports a conclusion consistent with PN law 44. Thus, examples like (75) are irrelevant to The Final 1 Arc Law. The kind of case which could be relevant to the truth of PN law 44 can be illustrated by such German examples as: (76) Hier here

wurde

getanzt

became

danced

= "One danced here, dancing took place here."

Such clauses evidently lack surface 1 arcs. This alone is no more rele­ vant than in (75). However, many writers on German syntax, e.g., Breckenridge(1975), Comrie (1977), would claim that such impersonal passive clauses have no 1 at all other than their initial 1. This can probably be taken to be the nominal man "one, ",deleted when the arc it heads selferases. Other writers might claim that such clauses have no Is at all. In our terms, however (see further discussion in Chapter 10), the struc­ ture of (76) is essentially the same as that of: (77) Es It

wurde

hier

became here

getanzt. danced

= "Dancing took place here."

230

7. FOCUS ON CLAUSE STRUCTURE

The key element of (77) is that is has a surface 1, namely, Es. For us the difference between (76) and (77) is, essentially, that in the former the 1 arc corresponding to Es self-erases, while in (77) it does not. This self-erasure is governed by, and interacts with, facts of constituent order­ ing. As is well known, German grammar demands that the dummy in cases like (77) appears only when, roughly, required to make the verb the second constituent in the clause. Hence, it does not appear in (76) where hier fulfills this function. In our terms, the 1 arc headed by the dummy will self-erase when a constituent distinct (from the dummy) precedes the verb. Self-erasure of the arc headed by the dummy thus effects word order, but, as previously remarked, provably has no effect on stratal structure. There­ fore, (76), like (77), would have a final stratum 1 arc and in no way vio­ late The Final 1 Arc Law. Our treatment of (76) is controversial, and there are many other cases where the preservation of The Final 1 Arc Law through appeal to selferased arcs headed by dummies is even more debatable. We will not attempt to deal with the relevant range of empirical issues here. The key point is that many different examples which might appear to violate PN law 44 do not do so under analyses in which such examples have final stratum 1 arcs (headed by dummies) which self-erase. We believe that this is the right analysis for all such cases. We should, however, take note of an inevitable objection. Some will argue that the appeal to the device of self-erased arcs headed by dummies renders The Final 1 Arc Law unfalsifiable. But this is incorrect. It simply renders it more diffi­ cult to falsify. There are, moreover, many interesting cases in which sur­ prisingly strong arguments can be provided for invisible dummies of the sort we have posited for (76), e.g., cases where they trigger agreement or undergo raising, etc. 22 It was stated earlier that we recognize clauses of a type not explicitly found in traditional grammar, intransitive clauses with initial stratum 2 22 This subject has been dealt with by D. M. Perlmutter and P. M. Postal, see initially Perlmutter and Postal (to appear a, to appear b, to appear c).

7.5. BASIC CLAUSES: NOMINALS

231

arcs. The Final 1 Arc Law offers a partial explanation of why this clause type is difficult to discern and why it has been generally overlooked. For, given this law, an initially intransitive clause whose initial Nuclear Term arc is a 2 arc cannot yield a well-formed clause unless there is also some 1 arc in the clause. Frequently, this can only be achieved if the 2 arc has a 1 arc local successor. There is a PN law which guarantees the existence of such a 1 arc successor in the relevant cases. By this we mean, in particular, that such a successor is justified independently of an individual grammar. This situation should be contrasted with the situation involving passivization. Here, 1 arc local successors for accusative

2 arcs are not required by any PN law.

To state the needed principle, referred to as The Unaccusative Law, it is necessary to define formally the notion Unaccusative, which we treat as a binary relation between an arc and the cj^th stratum of the tail of that arc. We take this occasion to define other related notions like Ergative, etc. For simplicity, let us introduce the following notation: (78) Abbreviation:

th Stratum (b) .

Then:

23 (79a).

The definitions in (79b-e) should be read in a fashion parallel to that in

232

7. FOCUS ON CLAUSE STRUCTURE

We are indebted to G. K. Pullum for suggesting the terms "unaccusative" and "unergative" to us. In these terms, an arc is ergative at a stratum if it is a 1 arc contrasting with a 2 arc at that stratum, the 2 arc in ques­ tion then being an accusative at that stratum. An arc is unergative at a stratum if it is a 1 arc but does not contrast with a 2 arc at that stratum. An arc is unaccusative at a stratum if it is a 2 arc not contrasting with a 1 arc at that stratum. Finally, an arc is absolutive at a stratum if it is a Nuclear Term arc which is not ergative at that stratum. 24 Hence, an arc is absolutive at a stratum if it is accusative, unaccusative, or unergative at that stratum. Given these concepts, which play a serious role in many phenomena, particularly but not exclusively those involving so-called ergative lan­ guages, we can move toward stating the law specifying the need for (certain) unaccusative arcs to have 1 arc local successors. First, how­ ever, we state a background law. This specifies that unaccusative arcs are "unstable," that is, that if an arc A is unaccusative at one stratum it cannot be unaccusative at the immediately successive stratum: (80) PN Law 45 (The Unaccusative Instability Law) Unaccusative (A, c^b)) -» Not (Unaccusative (A, Cj tfl O 3 ))) . 24 All these definitions take the notions to be r e l a t i v e to strata. Hence, it is logically possible for the same arc to be e.g., ergative at one stratum, and unerga­ tive, hence absolutive, at a later one, etc. Moreover, this is not only a logical possibility, but rather common. In (88c) below in the text, C is accusative at the ^2nd stratum. Similarly, a 1 arc absolutive at a c^th stratum is ergative at the c k i*h stratum if some Oblique arc has a 2 arc successor whose first coordinate + is , as in the following Dyirbal example from Dixon(1972): (i)

ba?7gul yayar?gu balan dyugumbil yanuman NC man NC woman went-with = "Man went with woman" In our terms, this has the relevant structure:

Com\c

barjgul yayangu

b a l a n dyugumbil

y a n u + man

7.5. BASIC CLAUSES: NOMINALS®

233

The rationale of this is as follows. We can infer from The Final 1 Arc Law that no unaccusative stratum is a suitable final stratum. Hence something must "happen" so that, for any given unaccusative stratum, there is a later stratum which is not unaccusative. There are two ways this can come about. The unaccusative arc can fall through into a later stratum but be accusative there, as the result of some other arc being ergative at that stratum. The other possibility is that an unaccusative arc can fail to fall through. We will speak of such unaccusative arcs as Evanescent. (81) Def. 132: Evanescent {A, c^b)) Unaccusative (A, cj^b)) λ Not (Accusative (A, c k + 1 (b») · The Fall-Through Law requires in this case that the unaccusative arc have a local assassin in the next stratum. PN law 45 simply generalizes these conditions to the maximum, i.e., it requires the "immediate" elimi­ nation of unaccusative strata from stratal families. It follows from (80) and (81) that: (82) Evanescent(A, c^b)) > (ΉΒ) (Local Assassinate (Β, Α) λ< Cj f f l β > (B)) This is a direct consequence of the fact that an arc evanescent at Cj f O 5 ) can only be consistent with PN law 45 by failing to fall through to c^ + 1 . The Fall-Through Law then guarantees that it must have a local assassin in the c^ +1 th stratum. The other logical possibility, namely, that Cj i defines the last stratum for node b is blocked by The Final 1 Arc Law. PN law 45 is formulated in such a way as to permit "rescuing" of un­ accusative arcs from its demands both by local assassination and by fol­ lowing stratum accusativity, because one possible "resolution" of insta­ bility is for an Oblique neighbor of an unaccusative arc to have a 1 arc local successor, rendering the unaccusative arc accusative at the immedi­ ately subsequent stratum. We suspect that this is the case in an example like (83a), which superficially contrasts with (83b), although we would assume they have similar initial arc structures. The relevant structure for (83a) is given in (83c):

234

t. FOCUS ON CLAUSE STRUCTURE

(83) a. This bottle contains 100 pills, b. 100 pills are in this bottle. c.

this bottle

IOO pills contains

Here C is unaccusative at C 1 but accusative at c 2 , and hence con­ sistent with PN law 45, although not locally assassinated. Of course, if this turns out to be an incorrect analysis of (83a) and, more generally, there are no cases of "accusativization" of unaccusatives as in (83c), PN law 45 could be strengthened to require that an arc unaccusative at c^(b) have Cjc as its last coordinate. This would block all structures in which unaccusative arcs are not locally assassinated, given The FallThrough Law and The Final 1 Arc Law. It would claim that all unaccusa­ tive arcs are evanescent. Consider now evanescent arcs, which, we know from (81), must be locally assassinated. There are various ways this condition can be met consistent with assumptions made so far and below. Our claim is that there is a fundamental if rather complicated condition which, in an impor­ tant class of cases, guarantees that evanescent arcs have 1 arc local successors. The local assassination of the evanescent arcs is then guaranteed by The Replacer Erase Law (for cases where copy pronouns exist, see Chapter 11) and by The Successor Erase Law in all others. The basic condition is roughly this. Some evanescent arcs "create" other unaccusative arcs—that is, they locally sponsor them, or locally sponsor other arcs which sponsor them, etc. In such cases, the evanes­ cent arc which "creates" an unaccusative does not have a 1 arc local successor. In all other cases, it does. Formally, "create" can be recon­ structed in terms of the ancestral of Local Sponsor, with the prefix Dto eliminate the case where the unaccusative arc is self-sponsoring (which

7.5. BASIC CLAUSES: NOMINALS

235

does not "rescue" it from the need for a 1 arc local successor). We thus propose the following as that element of APG theory which gives (some) evanescent arcs local 1 arc successors with no need for languageparticular rules: (84) PN Law 46 (The Unaccusative Law) Evanescent (A, Cj t O 3 )) a Not ((3B)(D-R-Local Sponsor (A, B) a Unaccusative(B, Cj(b)) a< C j/3> (B))) -> (3C)(Local Successor(C, A)a 1 arc C) . The antecedent of (84) has two conjuncts. Without the second, the law would require that all evanescent arcs have 1 arc local successors. What needs discussion are the reasons for postulating a weaker principle than that, in which only those evanescent arcs which do not "create" other unaccusatives are uniformly provided with 1 arc local successors. We cannot here explain these motivations in satisfactory detail, but they are based on the assumption that in many cases a single clause will contain more than one unaccusative arc. In these cases, we want at most one of the unaccusative arcs to have a 1 arc local successor. For exam­ ple, if an evanescent arc has a coreferential arc (see Chapter 11) replacer, the replacer will also in general be evanescent. We then only want the replacer to have a 1 arc successor. In this case, the replacee necessarily sponsors the replacer, and hence "creates" it, that is, D-R-Local Spon­ sors it. Such cases fall under PN law 46. Similarly, in some cases, a single clause has more than one organic unaccusative arc, and it is impossible for all of them to have 1 arc local successors. We only want the "last" evanescent arc to have this property. We illustrate this situation with an analysis of an English raising example, (85a) below. We take such sentences to involve an initial unaccusative complement. 25 The 1 arc of the complement then has a 2 arc successor 25 An argument for this view is that the relevant conditions defining raising involve a 2 complement, as in the case of raising with transitive verbs like believe, prove, etc. Thus, maximum generality is achieved in the statement of raising phenomena for English.

236

7. FOCUS ON CLAUSE STRUCTURE

in the main clause. This is the "raising." Thus, both the initial 2 arc and the immigrant 2 arc are unaccusatives, but only the latter has a 1 arc successor: (85) a. Melvin tends to lie. b.

55

Melvin

tends lie

In (85b), C is an initial unaccusative (evanescent) arc, that is, unaccusative at C 1 (SS). C has, according to principles clarified in Chapter 8, a Cho arc successor because of the existence of another 2 arc, B. B is also an unaccusative (evanescent) arc, that is, it is unaccusative at c 2 (55). B has the 1 arc local successor which PN law 46 requires. But, because C locally sponsors B, hence R-Iocal sponsors it, and in fact, D-R-Iocal sponsors it, C is not required to have a 1 arc local successor in this case, as desired. Hence, the restriction in the second conjunct of the antecedent of PN law 46 is designed, inter alia, to allow cases like (85b), in which a single clause has more than one organic evanescent arc. Another example of the same general type is provided by the Mohawk clause 26 in (86a), whose structure is found in (86b): (86) a. Sawatis John

[hra-

he

oobjective

nuhs-

a-

house

stem joiner

rak-

Λ

]

white perfective =

"John's house is white, John has a white house." 26 Such examples are discussed in an early transformational framework in Postal (1962).

237

7.5. BASIC CLAUSES: NOMINALS

b.

12

Sawatis

nuhs

hra-o-rtuhs-a-rak -Λ

In such examples, the final 1, Sawatis, is understood as the possessor of a nominal whose superficial reflex is in the incorporated noun stem nuhs.

Here there is a strong argument that the possessed nominal corre­

sponds to the head of an initial 2 arc. For it is a regularity of Mohawk that only initial 2 arc heads are candidates for incorporation. Both initial accusative and unaccusative heads trigger incorporation, but not initial ergatives or unergatives. In (86b), as in (85b), there are two organic un­ accusative arcs, B and C, both of which are evanescent. But only B has a 1 arc local successor. C does not fall under the scope of The Un­ accusative Law, because C is the local sponsor of the immigrant arc B. Hence, B is D-R-Local Sponsored by C . Again, according to the princi­ ples of Chapter 8, C has a Cho arc local successor, due to the "new" 2 arc, B. Although PN law 46 is stated in terms of the ancestral of Local Spon­ sor, all illustrations of the motivations for the relevant conjunct in the antecedent have been such that the evanescent arc without a 1 arc local successor sponsored another unaccusative arc. However, this is not always the case. An example where the ancestral is indeed required is provided by our analysis of so-called clause union constructions in Chapter 8, section 6. See in particular the discussion of (8.96b) there. Given analyses like that in (8.96b), one cannot simplify The Unaccusative Law and eliminate reference to the ancestral.

238

7. FOCUS ON CLAUSE STRUCTURE

Assuming The Unaccusative Instability Law and The Unaceusative Law both to be part of universal grammar, 27 these principles serve to dis­ guise the existence of initially unaccusative clauses. For they guarantee that either such unaccusatives will be accusative at more superficial strata, and hence disguised, or else must "create" other unaccusatives, etc., until one of these finally has a local 1 arc successor, and is hence disguised, disguising its "creators" as well. The Unaccusative Law guarantees that unaccusative clauses will be consistent with The Final 1 Arc Law and The Unaccusative Instability Law with no need for special language-particular rules. Even though evanescent arcs require local assassins, clauses can contain such with­ out imposing on individual grammars any onerous requirement for special rules to "fix up" these clauses. For even though evanescent strata can­ not "persist," there is a "free" method of assassinating them, namely, the presence of 1 arc local successors required by The Unaccusative Law. The 1 arc local successors required by The Unaccusative Law should be contrasted with the 1 arc local successors of accusative 2 arcs found in all of the kinds of passive clauses. Since there is no PN law which determines 1 arc local successors for accusative arcs, these successors may or may not exist in particular languages. Given The Final 1 Arc Law, the number of possible final stratum basic clause types involving Nuclear Term arcs is necessarily smaller than the number of initial or intermediate stratum clause types, because of the "instability" of unaccusative strata, given The Unaccusative Insta­ bility Law and The Unaccusative Law. Schematically:

27

In Postal (1977) the principle which requires (translating into APG terms) that an unaccusative arc have a 1 arc local successor is referred to as a univer­ sal rule. In the present framework, it makes no sense to speak about universal rules. If a principle expresses a genuine regularity about PNs in all languages, it is expressed as a PN law. If it does not, but is valid only for some particular language(s), it is naturally called a tale. See Chapter 14.

239

7.5. BASIC CLAUSES: NOMINALS

(87) Nuclear Term Arc-Determined Basic Clause Types

1 1

Initial and Intermediate Strata 2 1 2 Final Strata *2 2 1

Because of The Unaccusative Law, the initial unaccusative type normally 28 yields a final stratum of the unergative type. The Unaccusative Law not only plays a key role in the description of initial stratum unaccusative clauses, but also in the description of unac­ cusative strata found in various detransitivized constructions, including antipassive and inversion clauses. To illustrate, consider the latter, the construction in which an ergative arc has a 3 arc local successor. This is a productive situation in, e.g., Georgian, 29 where the existence of such a local successor is necessary in the evidential mode. Thus, there are examples like (88a), in which inversion is not relevant, which contrast with inversion clauses like (88b), the latter a perfect tense example be­ longing to Series III, which determines inversion. A partial structure of (88b) is given in (88c): (88) a.

deida aunt-Nom

myeris she-sing-I-3

naninas Iullaby-Dat =

"Aunt is singing a lullaby." b.

turme apparently

deidas

umyeria

nanina

aunt-Dat

she-sang-it-III-3

Iullaby-Nom =

"Apparently Aunt has sung a lullaby."

28

But not always, if, e.g., analyses like (83c) are valid for some clauses. 29Inversion in Georgian is discussed in detail in Harris (1976, 1977). In Harris (to appear) the case is made that inversion is a recurrent principle in vari­ ous unrelated languages.

240

7. FOCUS ON CLAUSE STRUCTURE

C.

deidas

ηαηιηα umyeria

In (88b) the initial 1, "aunt," appears in the dative case, the initial 2, "lullaby," in the nominative. The verb shows indirect object agreement with "aunt," further supporting its final 3hood. Interpreting Harris's (1976, 1977) analyses in APG terms, we take (88b) to involve a 3 arc local successor for the initial 1 arc and a 1 arc local successor for the initial 2 arc, as in (88c). That the initial 1 arc, B , has a 3 arc successor, A , defines an inversion construction and is mandatory in the relevant contexts in Geor­ gian (though precluded in others). Of direct interest is the existence of a 1 arc local successor, D, for the initial 2 arc. This is, as in initial unaccusative arc clauses, a function of The Unaccusative Law. Since C in (88c) is not accusative at c 3 , it is evanescent. Hence it could only fail to fall under the scope of The Unaccusative Law if it D-R-Sponsored an unaccusative arc, which it does not. Thus, in a clear sense, The Un­ accusative Law is "fed" by the existence of 3 arc local successor for an ergative arc. For, by providing the ergative arc with a local successor, it guarantees that the initially accusative arc (here C) is unaccusative at c 2 . Therefore, if we are correct, the existence of an inversion con­ struction, that is, of 3 arc local successors for ergative 1 arcs, guaran­ tees that the original 2 arc of such a construction has a 1 arc local successor with no need for special language-particular statements. 30 30 However, a fundamental problem lurks in this area, one implicit in a deci­ sion made, e.g., in (88c) but not justified so far. Namely, C in (88c) falls

241

7.5. BASIC CLAUSES: NOMINALS

A similar point is made by the structure of antipassive clauses like the Eskimo sentence in (89a) considered in Postal (1977), which would have the partial structure in (89b):

through from Cj to , and is unaccusative at C2> hence has a 1 arc local successor. The question is what precludes a representation in which C would not fall throu^i but would have a 1 arc successor whose first coordinate was C2 , instead of c^ as in (88c). There is another PN of the form: (i)

α

b

c

In (i), C is not unaccusative at any stratum and hence, the presence of its suc­ cessor 1 arc is not forced by The Unaccusative Law. Our claim would be that a PN like (i) involves both inversion and passivization; it has "simultaneous" local successors. We suspect that structures like (i) can exist (this problem is touched on in Chapter 8). The issue that is raised then is how an individual grammar distinguishes the two cases. More precisely, what is there about the grammar of Georgian which guarantees that its inversion construction involves PNs like (88c) and not those like (i)? There are grounds for denying that (88b) is a passive construction. Forpassivization exists independently of inversion in Georgian and involves a specific verbal morphology distinct from that in (88b). Thus, assuming that in certain cases inversion is compatible with passiviza­ tion and in other cases not, grammars must distinguish the two situations. We assume that it is proper to associate the differences with variants of inversion and that the differentiating condition is statable in terms of the concept Overran, introduced in the following chapter. A language like Georgian must have a rule specifying that the 1 arc local predecessor of a 3 arc must not be overrun by the local successor of a 2 arc (as D overruns B in (i)). Constructions of the form in (i) require a rule specifying, to the contrary, that a 1 arc local predecessor of a 3 arc must be overrun by the local successor of a 2 arc. Taking "X" to repre­ sent the factors defining the relevant constructions, these two "opposite" rules can be stated as: (ii) a. (For Georgian and other languages whose inversion constructions are incompatible with passivization) X Λ Local Successor (Α, Β) Λ 3 arc (A) Λ 1 arc (B) -» Not ((3C) (3D) (Overrun (C, B) ALocal Successor (C, D)A2 arc (D))). b. (For languages whose inversion construction necessarily involves "simultaneous" passivization) Rule identical to (iia) except that the Not is absent.

242

7. FOCUS ON CLAUSE STRUCTURE

(89) a.

gimmiq dog-Absolutive

miiqqa-mik

kii- si-

vuq

child-Instrumental bite-antipassive III singular =

"The dog bit a child." b,

gimmiq

mnqqa-mik

kii-si-vuq

Here the pair Successor(B, C) defines the antipassive construction. But this pair has the effect that, in (89b), B is unaccusative (evanescent) at C 2 (Il).

Since B does not D-R-Local Sponsor any unaccusative arc, the

conditions of The Unaccusative Law are met, and the pair Successor(A, B) is required. Hence, Eskimo in particular, and languages allowing antipassive constructions in general, need no special rules to insure the "readvancement" to lhood of 2s provided by the antipassive construction. We already illustrated a third case where The Unaccusative Law is "fed" by a construction and is relevant to a noninitial stratum, in the treatment of the Mojave predicate nominal clause in (51). The Mojave con­ struction in which an ergative (at Cj c ) arc has a P arc successor at

The clumsiness of such rules could be avoided by in effect talcing the conditions on the right-hand side of (ii), with and without negative, to define two contrasting types of 3 arc, types somewhat analogous to Ergative, Accusative, etc. Suppose the type in (iia) is called a Contrastive 3 arc, the type in (iib) a Simple 3 arc. The basis for this terminology is that the former type of 3 arc co-occurs in a stratum with a 2 arc, while the latter type does not. (iia,b) could then be re­ placed respectively by the more elegant: (iii) a. XALocal Successor(A, Β) Λ3 arc (A) Al arc (B) -> Contrastive 3 arc(A). b. XALocal Successor (A, B) A3 arc (A) Al arc (B) -» Simple 3 arc (A) . We will not bother to give the formal definitions of these terms here.

7.5. BASIC CLAUSES: NOMINALS

243

Cj tfl also, mutatis mutandis, creates a situation meeting the antecedent conditions of The Unaccusative Law. In sum, The Unaccusative Law is relevant not only for self-sponsoring arcs unaccusative at a particular stratum, but also for arcs which are unaccusative at a later stratum as a result of the fact that ergative arcs have various kinds of successors in inversion, antipassive, and other constructions. We have required that each basic clause contain an initial Nuclear Term arc and a final 1 arc. We have not, however, stated in any law so far an analogue for Nuclear Term arcs of The Basic Clause P Arc Con­ tinuity Law (PN law 41) for P arcs. Nothing so far shows that: (90) Every stratum of every basic clause contains at least one Nuclear Term arc. Such a principle can be formulated precisely along the following lines: (91) PN Law 47 (The Nuclear Term Arc Stratal Continuity Law) Cjth Stratum (b) φ. 0 Λ Point (b, Q) Λ Basic Cl Constituent(Q) ->

(3A) (Nuclear Term arc (A) λ A e c^th Stratum (b)) . We discuss PN law 47 further in Chapter 8, section 6. There we suggest that this principle can explain a hitherto unexplained gap in the class of so-called clause union constructions involving unaccusative complements. We have, of course, also not guaranteed that, e.g., a given basic clause has only a single 1 arc or a single 2 arc. As many previous struc­ tures show, there are endless cases where clauses (e.g., passives, antipassives, inversion clauses, etc.) involve more than one 1 arc, 2 arc, etc. However, we have also not guaranteed that a single basic clause has only a single 1 arc, 2 arc, or 3 arc at a given stratum. But we have illustrated no case where this type of constraint is violated. There is an RG principle which would guarantee this, that is, a princi­ ple which was part of the frameworks of both stage 1 and stage 2 RG. This has been called The Stratal Uniqueness Law (see Perlmutter and

244

7. FOCUS ON CLAUSE STRUCTURE

Postal [1977]). The essence of this can be "translated" into APG terms 31 as in (93) if we first introduce the following notational convenience: (92) Notation: Let Term x , Terniy , etc., be restricted variables over the set Term RS = {1,2,31 . (93) The RG Stratal Uniqueness Law "Translated" into APG Terms Term x arc (Α ΛΒ) Λ Neighbor(A, Β) Λ CJ C (AAB) -» A = B . (93) requires that if a Term arc is a member of some stratum S, no dis­ tinct arc with the same R-sign can be a member of S. In our current view, (93) is certainly true. However, in the present framework, much of the identity implicated in it is deducible from indepen­ dent assumptions. In particular, the claims of (93) turn out to be deduci­ ble for all strata other than the earliest strata containing arbitrary pairs of arcs like those mentioned in (93). Therefore, the proper course seems to be to state the relevant law only for earliest strata and to prove the re­ maining statement to be a theorem. Hence, instead of formulating (93) as a PN law, we instead state the apparently weaker: (94) PN Law 48 (The Earliest Strata Uniqueness Law) Term x arc (Α Λ Β ) A Neighbor (A, B) A (A) Λ < CJ C Β > (B) -> A = B . From PN law 48 and earlier assumptions, one can prove the content of (93): (95) THEOREM 55 (The Stratal Uniqueness Theorem) Term x arc (Α Λ Β ) Λ Neighbor (Α, Β ) Λ C J ^A A B ) -> A = B . However, the proof of (95) must be delayed until Chapter 8, which char­ acterizes Cho arcs in detail. The implication of Theorem 55 is that, while it is strictly meaningless to speak of the 1 arc, 3 arc, etc., of a clause, it is well defined to speak 31

In our translation, we make use of an identity statement about arcs. This is a stronger claim than the principle as understood in RG, which involved an identity of nodes. See Perlmutter and Postal (1977). In this respect, we are not so much translating, as correcting a mistake.

7.5. BASIC CLAUSES: NOMINALS

245

about the 1 arc of a stratum of a clause (if that stratum contains a 1 arc). A consequence of Theorem 55 is that rules, e.g., of agreement, which re­ fer to 1 arcs, etc., are only well defined if they pick out particular strata. For example, a rule which says that a verb agrees with the head of a 1 arc neighbor of the P arc of which the verb is head is ill defined, if in­ tended to pick out a unique nominal, unless the stratum of the 1 arc is specified. Hence, one normally finds that such agreements involve the final strata of clauses, although other specifications, e.g., initial, are not unknown.

Ο Λ

We have required each basic clause to contain an initial Nuclear Term arc and a final 1 arc, imposed a condition of identity on neighboring Term x arcs sharing their earliest coordinates, stated that these and earlier assumptions entail stratal uniqueness for Term arcs with respect to all strata (but postponed the proof until Chapter 8) and specified (see PN law 47) that all strata of basic clauses contain Nuclear Term arcs. These are, to our knowledge, the major general necessary conditions to be imposed on basic clauses with respect to Nominal arcs. We have concentrated the discussion on 1 arcs and 2 arcs because there is a real sense, expressed in PN laws 43 and 44, in which they are central to basic clause structure. If these laws are correct, then, simply put, there are no basic clauses without initial Nuclear Term arcs and none without final 1 arcs. However, clauses may also contain 3 arcs. Under current assumptions, 3 arcs may occur in initial, intermediate, and final

strata. The italicized hedge is meant to suggest our view that it would not be surprising if it ultimately turned out that there were no initial (selfsponsoring) 3 arcs. But as we are not at present in a position to offer and support reasonable analyses for all cases of 3 arcs which we now take to be initial 3 arcs, this remains a conjecture. Since 3 arcs are Term arcs, they fall under The Stratal Uniqueness Theorem.

^Verbal agreement with initial Is is described for Achenese in Lawler (1977) and for Kapampangan in Mirikitani(1972).

246

7. FOCUS ON CLAUSE STRUCTURE

(87) above gives a rough typology of basic clause types which, how­ ever, ignores 3 arcs. Significantly, and supporting the view that possibly there are no self-sponsoring 3 arcs, it seems that the addition of 3 arcs to (87) yields a clearly attested type of initial 3 arc of only the transitive sort, the traditional bitrarisitive or ditransitive clause, like French: (96) Marie

a

Marie has

montre Ie true

a Jacques.

shown the "thing" to Jacques = "Marie showed the

'thing' to Jack." We know of no cases where one would want to analyze the initial strata of clauses as containing either (i) a 1 arc and a 3 arc but no 2 arc; or (ii) a 2 arc and a 3 arc but no 1 arc; or, of course, given PN law 43, just a 3 arc. (97) Self-Sponsoring(Initial) Term Arc-Determined Clause Types 1 2

3

*1 3

*2

3

*3 .

However, strata of the second type can exist as intermediate and/or final strata, e.g., in examples like: (98) I talked to Jeremy. where there is a final 1 arc and a final 3 arc. Many grammarians would in effect claim that examples like (98) should be analyzed as involving an initial stratum in which there are, with respect to Nominal arcs, just a 1 arc and a 3 arc and hence, contrary to (97), an instantiation of the second type in (97). However, we suggest that this is mistaken and that all examples like (98) involve as well a self-sponsoring 2 arc, whose head corresponds to a unique (unspecified) nominal of the type referred to as UN in Chapter 10. It is notable that such examples inevitably seem to have near paraphrases of the ditransitive type: (99) I 'talked to Johnny = I said

something^ to Johnny .

wrote

wrote things

\

sang

sang

)

7.5. BASIC CLAUSES: NOMINALS

247

In our view, (97) is not incompatible with the common existence of clauses whose only final Nominal arcs are a 1 arc and a 3 arc of the type: (100) That matters to me. For we take all such clauses to be (lexically determined) instances of the inversion construction (discussed above in connection with Georgian), which involves a 1 arc having a 3 arc local successor, "feeding" The Unaccusative Law. Hence, we would analyze examples like (100) at the initial stratum as involving a 1 arc whose head corresponds to me and a 2 arc whose head corresponds to that. (100) would thus involve no selfsponsoring (initial) 3 arc at all, the final 3 arc being a successor of the initial 1 arc. (100) would then be of initial stratum type three in (87) and irrelevant to the claims in (97). Similar remarks would hold for examples like (101), also involving final 1 arcs and 3 arcs: (101) a. French Cela that

m'importe. me Q

b. Spanish Me

a ^ ve I

s

important = "That is important to me."

gusta eso.

me n . likes that = "I like that." Dative c. Japanese (from Kuno [1973a: 338]) John ni

nihongo ga

dekiru.

John r , .. Japanese,,, . can Dative F Nominative d. Russian jej

nuzna

= "John can speak Japanese.'

praktika

. necessary practice,. = "She needs Dative Nominative

Sher.

practice.'' If, as seems plausible, the only cases of self-sponsoring 3 arcs under present assumptions are those in ditransitive examples like (96), this makes more likely the view that there are ultimately no self-sponsoring 3 arcs. For there are independently needed APG principles which determine certain immigrant arcs as ditransitive 3 arcs, e.g., in clause union con­ structions like that illustrated by French:

248

7. FOCUS ON CLAUSE STRUCTURE

(102) Marie a laisse lire la lettre a Claude. Marie has let read the letter to Claude = "Marie let Claude read the letter." (Also "Marie let unspecified read the letter to Claude.") Here the node corresponding to Claude is (under the first reading in the translation) the head of an immigrant 3 arc determined regularly by prin­ ciples for clause union constructions (constructions involving U arcs). 33 It is not inconceivable that all ditransitive 3 arcs could ultimately have the same (foreign successor) origin as this 3 arc, eliminating all selfsponsoring 3 arcs. But we leave this as a conjecture, assuming for practical purposes at the moment that there are initial 3 arcs of at least the ditransitive type. In addition to being the tails of Term arcs, basic clause nodes may, of course, also serve, under current assumptions, as the tails of initial, intermediate, and final strata Oblique arcs, that is, Loc arcs, Temp arcs, Inst arcs, Ben arcs, etc. The grammatical relations these represent are the least understood in the domain of nominal-clausal relations, and we have relatively little to say about the corresponding arcs here. The itali­ cized hedge in the first statement of this paragraph is meant to suggest our view that ultimately it is likely that no Oblique arcs will be initial arcs, all nongraft Oblique arcs being immigrant arcs. But as we do not know how to construct viable analyses in these terms at the moment, we also leave this as a conjecture for the future. 34 At the moment then, we would analyze (103) Melvin tickled Sally with a feather.

OO

These are dealt with briefly in Chapter 8, section 6. ^The idea implicit here is that, e.g., what we now take to be a self-sponsoring Loc arc is really an immigrant arc with some independently needed R-sign, which is a successor of a Central arc, probably a Nuclear Term arc, which is the neigh­ bor of a P arc involving a locative predicate. Schematically then (i) might be represented as (ii):

7.5. BASIC CLAUSES: NOMINALS

249

as involving a self-sponsoring Inst arc with the same tail as the 1 arc and 2 arc whose heads correspond to Melvin and Sally. Certain questions then are raised at this point. Can there, under current assumptions, be any nongraft Inst35 arcs whose first coordinates are not Cj ? Or, in other terms, can Oblique arcs ever be the successors of other arcs? This is perfectly possible logically and nothing said so far excludes it. Oblique arcs as successors are permitted for the same reason that 1 arcs can be the (local or foreign) successors of 2 arcs, and 2 arcs the successors of Ben arcs, etc. It seems, however, that Oblique arcs can never be succes­ sors (either local or foreign). We introduce this claim as the following law: (104) PN Law 49 (The No Oblique Successors Law) Successor (A, B) -> Not (Oblique arc (A)) .

(i)

Joe sang under the porch.

LOCATED

GR the porch Joe

song

Thus, what we now take to be a Loc arc would actually be a GR x arc successor of a "higher" 2 arc neighbor of a P arc whose predicate is LOCATED. This ignores the extra specification of "under" in (i). In these terms, the specificity of each Oblique R-sign would derive from a specific logical predicate in some superordinate structure. In such an approach, the equivalents of Oblique arcs would be defined concepts. There would be no Oblique R-signs, only a much smaller (possibly unary) set of R-signs like GR x in (ii). Some revision of PN law 51 would then be necessary, given structures like (ii), in which a Nominal arc successor has an arc commanding predecessor. 35 Flagging phenomena and pronominalization involve graft arcs of all the Oblique types. Naturally, none of these are Cj arcs.

250

7. FOCUS ON CLAUSE STRUCTURE

This constraint indicates that all the domestic Oblique arcs in a clause are self-sponsoring and that there can be no immigrant Oblique arcs. 36 Thus, the only non C1 Oblique arcs allowed in these terms are grafts. These do exist as a result of general principles relevant for, inter alia, nominal flagging, "pronominalization," etc.: (105) Mary, John will never do anything for her. (105) involves, in current APG terms, a graft Ben arc whose head is the nominal node corresponding to her, as well as a self-sponsoring Ben arc whose head corresponds to Mary. In addition, Mary is the head of an Over­ lay arc, namely, a Top arc. Earliest versions of RG involved a principle referred to as The Reranking Law. If we translate the claims of this principle into present terms,

O hJ

we can say that The Reranking Law claimed essentially the following: (106) The RG Reranking Law Partially "Translated" into APG Terms Nominal arc (A)

Λ

Nominal arc (B)

Λ

Successor (A, B) -> Outrank (A, B) .

The notion Outrank was intended to be understood as a transitive relation such that, translating into APG terms, neighboring arcs were assigned a rank according to a hierarchy of R-signs, as follows: (107) 1 outranks 2 outranks 3 outranks ICho [any member of Oblique RS 36 Of course, in pursuing an approach like that in note 34, this law would have to be modified totally, leading to something of the reverse claim. All of what are now organic Oblique arcs would become immigrant arcs instead of being self-sponsoring. But it would still be true that the only "Oblique" successors allowed would be those defined by configurations like (ii) in note 34. It would remain impossible to, e.g., give a 1 arc a local Inst arc successor, etc. 37 No really accurate translation is possible. In particular, (106) ignores the fact that the RG Reranking Law was supposed to be a constraint on rules, while in RG chomeurs were not introduced by rules but by a universal law not covered by The Reranking Law. Hence, (106) says in effect that Cho arcs cannot be suc­ cessors of Term arcs (although all domestic Cho arcs are such successors), quite in conflict with the spirit of the RG principle, because (106) is a principle about PNs .

251

7.5. BASIC CLAUSES: NOMINALS

Nonneighboring arcs were assigned a relative rank only if the tail of one R-governed the tail of the other. In this case, the arc with the R-governing tail was higher in rank. We can formally introduce the notion of Outrank, insofar as this is relevant to neighboring arcs, as follows. First, we introduce SignPrecedence as a binary relation between R-signs: (108) Def. 133: Sign Precede (X, Y) *-* (i) (ii)

X = I aY = 2, or X e Nuclear Term RS Λ Y = 3, or

(iii) X € Term RS

Λ

Y / Term RS.

Then we can define "Outrank" as a predicate of APG: (109) Def. 134: Outrank(A i B) -Xarc(A)AYarc(B)ASignPrecede(X 1 Y). We introduce Outrank, even though it plays only a marginal role so far. In particular, in abandoning The Reranking Law, we lose that motivation for the concept. However, there is one law now statable which does depend on Outrank. We introduce this here, although its real relevance is not naturally describable until later chapters: (110) PN Law 50 (The Demotion No Replacer Law) Local Successor(A, Β) λ Outrank (Β, A)

Not ((3C)(Replace (C, B))) .

This law precludes local "demotion" constructions from containing copy pronouns. PN law 50 allows there to be a plain passive or a so-called re­ flexive passive construction involving pairs of the form Local Successor (1 arc, 2 arc), there being in the latter case in addition a 2 arc headed by a copy pronoun. This 2 arc is a replacer and hence erases the prede­ cessor 2 arc. But PN law 50 does not allow the analogue in cases of, e.g., antipassive, inversion, and, in particular, in those cases where a Term arc has a Cho arc successor. Thus, an entailment of PN law 50 is that local predecessors which outrank their successors are invariably erased by their successors, since they can have no replacers. We will discuss the implications of PN law 50 in Chapter 8.

252

7. FOCUS ON CLAUSE STRUCTURE

Returning to The Reranking Law, observe that this principle and The No Oblique Successors Law are logically disjoint, although the former has as entailments most of the consequences of the latter. In particular, both principles correctly prevent situations in which an Oblique arc is a succes­ sor of a neighbor arc. However, The Reranking Law does not preclude (although it was intended to preclude, and wrongly assumed to preclude) cases where an Oblique immigrant arc A is a successor of, e.g., a Term arc, B, with A in a "higher" clause than B. TheRerankingLawdoes not, for example, preclude a construction analogous to "subject raising" in which, however, the immigrant arc of relevance is an Oblique arc. Since such cases are unattested, The Reranking Law is, in this respect, ioo weak, although PN law 49 is not. However, in another direction, The Reranking Law is much stronger than The No Oblique Successors Law. Only the former blocks all cases of the following type: (i) Local Successor (3 arc, 1 arc); (ii) Local Succes­ sor (3 arc, 2 arc); (iii) Local Successor (2 arc, 1 arc). However, as already partially indicated, all of these "demotion" successor types are attested. Thus, (i) holds in the case of an inversion construction and (iii) holds in our account of antipassivization. This is another reason for abandoning any version of The Reranking Law. The No Oblique Successors Law, like the abandoned Reranking Law, establishes a fundamental asymmetry among Core arcs. Given this law, Oblique arcs can have Term arc successors, but not conversely. Therefore, Oblique arcs enter into successor pairs only as predecessors, while Term arcs can be both predecessors and successors. This asymmetry, together with the necessity of initial Nuclear Term arcs, accounts for the central role played by Term arcs in the description of basic clause structure. This role is elaborated in the following chapters, when we discuss the status and properties of Cho arcs, which depend on Term arcs. Before leaving Oblique arcs, we should raise a question parallel to the issue of stratal uniqueness for Term arcs. Can a single stratum contain two distinct arcs with the same Oblique R-sign? We doubt that this is possible. Apparent counterexamples like:

7.5. BASIC CLAUSES: NOMINALS

253

(111) I bought the book for Ted for Martha. where a superficial view might claim there are two Ben arcs, seem specious. Investigation reveals that the two /or phrases in such cases have quite different properties. The leftmost represents the intended recipient of the object designated by the initial 2 arc head, while the rightmost represents the benefactor of the action. In our terms, only the latter is the head of a Ben arc. Further, only the former involves an arc which can have a 2 arc local successor: (112) I bought Ted the book for Martha. Here Martha continues to be the one for whose sake the action was done, not the intended recipient. English does not freely permit Ben arcs to have 2 arc successors, 38 although this is relatively productive for what­ ever kind of arcs involve intended recipients. We suspect, then, that a principle of stratal uniqueness for Oblique arcs is valid. But, as we have not studied this area seriously, we will not formulate a PN law to this effect. There is an important limitation on the current account of basic clauses. We have required basic clauses to "contain" initial Nuclear Term arcs, final 1 arcs, and a Nuclear Term arc in every stratum. We have in addition claimed that basic clause strata meet a condition of stratal uniqueness for Term arcs and speculated about a parallel condition for Oblique arcs, whose presence in basic clauses is allowed but not demanded. Moreover, we eliminated the possibility that Oblique arcs could be successors. Al­ though this amounts to an important set of constraints on the kinds and combinations of arcs which can have basic Cl constituent points for tails, it is far from a complete theory. In particular, we have not been able to OO

It does have such constructions in lexically determined cases, e.g., with the do of do a favor. (i)

I did a

Iiavor/

(ii) I did Joe a

for Joe.

254

7. FOCUS ON CLAUSE STRUCTURE

impose constraints which would fully specify (by R-sign) the class of arcs which can have basic Cl nodes for tails. We know that this set in­ cludes Term arcs, Oblique arcs, Dead arcs, Cho arcs, and P arcs, but we have imposed no PN laws which limit the relevant class to just these. Moreover, when one considers adverbs, floating quantifiers, "extraposed" relative clauses, etc., it seems that the class of possibilities is richer than this. But obviously there are a limited number of arc types beyond those just enumerated which can have basic Cl nodes for tails, and one can look forward to the day when an exhaustive enumeration of this class becomes possible. Although we have not limited the class of arcs with basic Cl nodes as tails, it might be possible even now to limit the local successor types for certain classes of arcs, e.g., Core arcs. Our analysis of predicate nominal clauses above allows P arc successors for certain Core arcs. Aside from this, however, we know of no local successors for Core arcs which are not Central arcs, and a claim that this is a law seems currently warranted. However, we delay formulating this as a PN law until the end

of the next chapter, where we can use the law and other results of Chapter 8 to prove an important consequence (see Theorem 74). In retrospect, The Heranking Law involved some correct insights but some mistakes as well. The chief insight with respect to neighboring arcs is, we claim, now represented by The No Oblique Successors Law. But there is a major problem with our translation of The Reranking Law as (106), as already discussed in note 37. Namely, (106) would not permit a Term arc to have a Cho arc local successor. But, as considered in Chap­ ter 8, this is the source for all organic Cho arcs. We have already pointed out how, with respect to nonneighboring arcs, The Reranking Law involved the mistake of permitting Oblique arcs to be foreign successors. We now consider what we take to be one further insight about nonneighboring arcs implicit in The Reranking Law. This implies, in APG terms, that there are asymmetries in Nominal arc successor pairs, where the successor is an immigrant arc.

The basic claim involved in The Reranking Law for cases where rela­ tive rank was determined in terms of something like the predicate R-govern

255

7.5. BASIC CLAUSES: NOMINALS

is that Nominal immigrant arcs are invariably found in "higher" clauses than their predecessors. Or, in a more traditional terminology, although there are "raising" constructions involving nominals, there are no attested cases of "lowering" constructions involving nominals. Hence, there are clause union constructions like French: (113) Pierre

fera

accomplir

la

Pierre make-will accomplish

the

tache task

aux

enfants.

to the children =

"Pierre will have the children accomplish the task." in which there is a main clause immigrant 3 arc whose head corresponds to the nominal enfants and whose predecessor is the complement clauses 1 arc. However, there are no "opposite" cases. It is easy to formulate artificial examples which would be "opposite" in this sense. What would be relevant is, e.g., the existence of examples like (114a) with the meaning and initial arc structure of (114b): (114) a. *Melvin told that Ted sang Mary. b. Melvin told Mary that Ted sang. In our terms, (114a) would involve a complement clause immigrant 2 arc as successor of a main clause domestic 3 arc. 39 The structure of (114a) would be essentially:

fold

Melvin

Mary Ted

sang

^TeIl occurs in clauses with initial 1, 2, and 3 arcs. The 3 arc can have a local 2 arc successor, as in (114b), and this is indeed mandated under many circumstances, including those where the head of the initial 2 arc corresponds to a that complement. This is why we represent Mary as a 3 in (115).

256

7. FOCUS ON CLAUSE STRUCTURE

Such structures are perfectly possible logically and violate none of the conditions on PNs so far imposed. 40 Since they do not occur, some fur­ ther law(s) must be found to exclude them. It would be easy enough to exclude all cases where an immigrant arc is in a "lower" clause then its predecessor, that is, to exclude all "low­ ering." But such a constraint is much too strong. Elements like quanti­ fiers, comparatives (more), etc., have positions in S-graphs which are "lower" than their positions in L-graphs. For a sentence like: (116) I tickled each of the kangaroos twice. the nonterminal node corresponding to each is governed by a nominal node which is governed by the clause node serving as the tail of the P arc whose head corresponds to tickled. However, the L-graph of (116) must have the node corresponding to each as an operator which has the open sentence corresponding to the tickle clause as one of its components. The position of the each node in the L-graph is "higher" than its position in the S-graph of (116). Consequently, "lowering" is a necessity. In APG terms, one arc with the each node as head will have a "lower" arc as foreign successor. To understand the difference between cases like (115), where "lower­ ing" is unattested, and (116), where "lowering" is standard, it suffices, we believe, to observe the differing R-signs of the immigrant arcs in the two cases. In the blocked situations, the immigrant arc would have an R-sign which is a member of Nominal RS , while in cases like (116) this would certainly not be the case. We conclude that it is a plausible hy­ pothesis that "lowering" is blocked for Nominal immigrant arcs. We might express this formally as: (117) Nominal arc (A)

Λ

Successot(A j B)

R -govern (Tail (A), 40

Λ

Immigrant arc (A) ->

Tail (B)) .

It might be argued that the immigrant arc has no ''natural" local sponsor. But in the absence of a theory of possible local sponsors, this is without much force-

7.5. BASIC CLAUSES: NOMINALS

257

However, the last conjunct of the antecedent of (117) is redundant. For when Successor(A j B) and A is not an immigrant arc, the two arcs share tails. But every node R-governs itself (since R-govern is the an­ cestral of Govern, and all ancestrals are reflexive relations). Consequent­ ly, one can, without unwanted consequences, eliminate the reference to Immigrant arc. Moreover, evidently the consequent of (117) is rather clumsy. We hence introduce terminology to permit elimination of the refer­ ence to nodes: (118) Def. 135: Arc Commands (A, B) «-» R-govern (Tail (A), Tail (B)) . In these terms, a "raising" construction is one involving foreign suc­ cessors which arc command their predecessors; a "lowering" construction is one having foreign successors arc commanded by their predecessors. We restate (117) as: (119) PN Law 51 (The Nominal Arc Successor Law) Nominal arc (A)

Λ

Successor (A, Β) -> Arc Commands (A, B) .

Notice that this law imposes no constraints on Nominal arc predecessors. It does not preclude the case where a Nominal arc has a successor which is not a Nominal arc and which does not arc command its predecessor. While such cases are highly restricted, we believe they do exist. They are discussed in Chapter 13. Although we have introduced PN law 51 in terms of blocking Nominal arcs which are "lower" than their predecessors, its implications are far more general. It also blocks the vast set of unattested, though logically possible, cases in which, e.g., an immigrant arc of the relevant type in one conjoined clause has a predecessor in another conjoined clause; where an immigrant arc of the relevant type in a relative clause on a sub­ ject has its predecessor in a relative clause on an object, or vice versa, etc. In short, there is a mass of cases distinct from "lowering" where an immigrant arc fails to arc command its predecessor, and all of these are blocked by PN law 51 for Nominal arc successors.

258

7. FOCUS QN CLAUSE STRUCTURE

There is at this point much too much freedom allowed in cases of suc­ cessors which are not Nominal arcs. This is related to our rejection of a total ban on all "lowering," For, while "lowering" is required for quanti­ fier elements, it is not clear that there are any cases where, e.g., quanti­ fiers, comparative elements, etc., are the heads of immigrant arcs which are not arc commanded by the tails of their predecessors. That is, the successor pairs in these cases are the opposite of those in cases of Nomi­ nal arc successors. In quantifier situations, it seems that the successor arc must be arc commanded by its predecessor. But nothing so far guaran­ tees this. This simply points up the need for many further laws governing successor pairs. But as we have not studied the domain of successors outside of the realm of Nominal arcs to any extent, we will not pursue this matter here. To conclude this section, we offer two further proposals. First, the question arises as to what kind of nodes can be the tails of Central arcs. We suggest that the answer is only basic clause nodes. (120) PN Law 52 (The Central Arc Tail Law) Central arc (A)

A

Tail (a, A) -> (JIQ) (Basic Cl Constituent(Q) A Point (a, Q)) .

Inter alia, (120) claims that there cannot be Term arcs, etc., whose tails are nominal nodes, etc. Thus it rules out the possibility 41 of analyzing a nominal like (121a) as involving a 1 arc whose tail is the nominal node: (121) a. Melvin's attack on Greta. b. Melvin attacked Greta. If, as seems correct, it is true that Melvin in (121a) is the head of a 1 arc just as in (121b), The Central Arc Tail Law requires that (121a) involve a clause constituent, with Melvin heading some other (immigrant) arc whose

41 That is, it rules out an APG analogue of the proposal by Chomsky (1970) that the structure of nominals involves similar relations to the structure of clauses.

7.5. BASIC CLAUSES: NOMINALS

259

tail is the nominal node. That is, (120) mandates a "nominalization of clauses" approach to nominals like (121a). Given The Central Arc Tail Law, Central arcs and basic Cl Constituents co-occur. The SelfSponsoring Nuclear Term Arc Law requires every basic clause node to be the tail of a Nuclear Term (hence Central) arc, while PN law 52 requires the tail of every Central arc to be a basic Cl constituent point. Our second proposal is fairly obvious but so far not mandated. We have been developing a theory of possible PNs and have lately discussed basic Cl constituents. But we have said nothing which guarantees that a PN "contain" such a constituent. This seems to be a valid condition on such: (122) PN Law 53 (The PN Basic Cl Constituent Law) Y = Arc Set (ΡΝχ)

(3Q)(QC Y ABasic Cl Constituent(Q)) .

As it stands, (122) is rather uninteresting and suspect since it does not "localize" the basic clause constituent. In particular, it does not say that the point of the whole arc set of a PN is a basic clause node. It would be easy enough to say this formally, and we suspect that it is cor­ rect. However, in a wide class of cases, such a stronger principle re­ quires recognition of an array of structure without S-graph realization, and involves many problems related to transformational discussions of in­ visible performative analyses, etc., topics which go beyond the scope of this discussion. We thus terminate our claims with PN law 53 at this stage. 7.6. Overlay arcs and clause structure There is a vast literature in the transformational framework on socalled "unbounded movement rules," designed, inter alia, to account for properties of examples like: (123) a. Tom, I like. b. Tom, I think I like.

260

7. FOCUS ON CLAUSE STRUCTURE

c. Marsha said that Tom you would like. d. Who does Fred like? e. Who did Martha say Fred liked? f. the gorilla which Fred likes ... g. the gorilla which Fred says Martha likes ... In such examples, there are nominals occurring in positions not "expected" given their representation in terms of Central arcs alone. Thus, e.g., in (123a,b,c), the nominal node corresponding to Tom is the head of a 2 arc whose tail is the clause node involving like as its predicate. Such nomi­ nal nodes are normally positioned following the V of their clauses. It is evident that in cases like (123 a-c) and all similar examples, further state­ ments are necessary to account for, among other things, the distribution of the nominals in question. The domain of facts exemplified by (123) is one on which little work was done in RG terms and little has also been done in APG terms. We would, nonetheless, like to sketch a general approach to this area consis­ tent with the rest of the framework under development. Our essential idea is that examples like (123) involve arcs associated with one of the R-Signs referred to in (6) as members of Overlay RS; hence these examples involve Overlay arcs. We consider some properties claimed to be associated with such arcs. First, Overlay arcs are restrict­ ed in terms of the basic arc typology of domestic, immigrant, and graft. (124) PN Law 54 (The Overlay Arc Status Law) Overlay arc (A) Λ Not (Immigrant (A)) -» (3B) (Replace (A, B)) . This law thus permits nonimmigrant Overlay arcs only in the single case where these are replacers. Most of the data familiar to us would be con­ sistent with an even stronger principle than (124) which would simply say that all Overlay arcs are immigrants. However, some data from Afrikaans cited in du Plessis (1977) indicates that certain Overlay arc predecessors have copy arc replacers (see Chapter 11 for this notion). The data from

7.6. OVERLAY ARCS AND CLAUSE STRUCTURE

261

Afrikaans is also incompatible with other apparently valid generalizations about Overlay arcs and thus deserves close scrutiny. However, seeing no way to keep such data consistent with nonreplacer Overlay arcs, (124) is the strongest principle we can currently adopt. PN law 54 determines that there can be no domestic Overlay arcs: (125) THEOREM 56 (The Overlay Arc Status Theorem) Overlay arc (A) -» Not (Domestic (A)) . Proof. Let A" be an Overlay arc. PN law 54 determines that if A' is not an immigrant, it is a replacer, and hence a graft. Theorems 25 and 28 indicate that the sets of domestic arcs, immigrants and grafts are disjoint. QED. Thus there can be no Overlay arc local successors nor any self-sponsoring Overlay arcs. Since all replacers are cosponsored, it also is true that all Overlay arcs have two sponsors, this being an invariant feature of immi­ grant arcs in the current system. The second constraint on Overlay arcs has to do with the kind of nodes which can be tails of Overlay arcs. As things stand, nothing prevents Overlay arcs from having tails which are points of basic clause constitu­ ents and thus, e.g., neighbors of 1 arcs, 2 arcs, etc. We believe, how­ ever, that this is not possible and that Overlay arc tails are points of special types of constituents, which are incompatible with basic Cl con­ stituents. Recalling that the latter must be inherent, that is, tails of at least one self-sponsoring arc, we suggest that tails of Overlay arcs can only be the tails of noninherent arcs. (126) PN Law 55 (The Overlay Arc Tail Law) Overlay arc (A) A Tail (a, A) -> Not (Inherent (a)) . From this, it follows trivially that:

(127) THEOREM 57 (The Overlay Arc Tail/Basic Cl Node Incompatibility Theorem) Overlay arc(A) a Tailip.,A) -> Not((3.Q)(Basic Cl Constituent(Q) λ Poinf(a,Q))).

262

7. FOCUS ON CLAUSE STRUCTURE

Proof. Let A' be an Overlay arc whose tail is a'. It follows from The Overlay Arc Tail Law that a' is not inherent. If, contrary to the conse­ quent, a' were the point of a Basic Cl Constituent, a' would, however, have to be inherent, since all basic constituent points are by definition inherent. QED, Under the assumption that nominals like Tom in (123a-c) are heads of Overlay arcs, The Overlay Arc Tail Law entails that the Overlay arc tail is distinct from the tail of the basic clause involving like as predicate. We are thus forced to analyze, e.g., (123) partially along the following lines:

GR.

Top

66

Tom

I

like

Here A is the Overlay arc, C its foreign predecessor. The Overlay Arc Tail Law requires that node 95 not be the tail of any self-sponsoring arc. Hence B cannot be self-sponsoring. We return in Chapter 13 to the ques­ tion of the sponsors of certain arcs like B . A further straightforward consequence of PN law 55 is that Overlay arcs and Central arcs can never be neighbors: (129) THEOREM 58 (The Overlay Arc/Central Arc Nonneighbor Theorem) Overlay arc (A)

Λ

Central arc (B) -» Not (Neighbor (A, B)) .

Proof. Let A' be an Overlay arc and B' be a Central arc. It follows from PN law 52, The Central Arc Tail Law, that the tail of B' is the point of a basic Cl constituent, hence an inherent node. But PN law 55 determines that the tail of A' is not inherent. QED.

263

7.6. OVERLAY ARCS AND CLAUSE STRUCTURE

Thus, there can, e.g., be no constructions otherwise analogous to attested raising or clause union constructions in which the immigrant arcs are not Term arcs but Overlay arcs. In many, but not all cases, we would assume that the tails of Overlay arcs are nodes associated with the structure of so-called complementizer forms.42 (128) is such a case, but this is obscured because the relevant arc P-headed by a complementizer self-erases. Let us consider instead the structure of an example like (130a) given in (130b): (130) a. Marsha said that Tom you would like. b.

f

Marsha

/

that

Xi

Tom

ι

you

ι

(would) like

Here G is the Overlay arc, an immigrant arc locally sponsored by K, a Marq arc, and foreign sponsored by its predecessor, H. The key element in this structure is that the complement clause node, which is the tail of J , occurs as head of a Marq arc, in addition to occurring as expected as the head of a 2 arc. The structure composed of the Matq arc K and the F arc E establishes, in our terms, the existence of a complementizer for the complement. Thus, we regard complementizer morphemes as P-heads 42 This aspect of our treatment of these phenomena thus shares certain abstract similarities with the transformational proposals in the recent work of Chomsky (1973, 1975b, 1977).in which rules like Wh Movement move elements under Comp nodes.

264

7. FOCUS ON CLAUSE STRUCTURE

of F arcs whose tails have the following property: they are also tails of Marq arcs. F arcs and Marq arcs are discussed further in Chapter 13, where it is required that they co-occur. As indicated earlier, we take the Top arc in this structure to have as tail the tail of the F and Marq arcs. Thus, it follows from PN law 55 that the point of a complementizer constituent, node 50 in (130b), must not be inherent. Hence, the relevant arcs can have no self-sponsoring neighbors. We have specified nothing about the grammatical category which nodes like 50 in (130b) belong to. In (130b), the node in question must probably be labeled Nom. This follows since The Central Arc Head Label Law specifies that entrant Central arcs whose heads are not labeled Cl must be labeled Nom. B in (130b) is a Central arc and an entrant (since it is a replacer). Therefore, B's head could fail to be labeled Nom only if it is labeled Cl. We have given no principle which labels 50 as Cl and doubt there is any. This suggests the possibility of a law which would prevent nodes like 50 from being labeled Cl. If such a law can be formulated, it would render the Nom labeling of nodes like 50 a theorem. Hence, it would turn out that the point of that Tom you would like would be labeled Nom even though the internal complement would be labeled Cl. This seems an acceptable result. A key feature of (130b) is B , a type of arc called a closure. This concept is formally defined in Chapter 13, where a law is stated to guaran­ tee the introduction of such in cases like (130b). Closures are a subset of grafts which serve to permit structures like (130b) to define well-formed S-graphs. Without B, which erases C, the tail of J is the head of two distinct otherwise unerased arcs, K and C . But such a structure does not meet the tree conditions imposed on the structural arcs of surface sentences (see (4.29e), The S-graph SS Condition), since a tree cannot contain any nonterminal nodes which are the heads of more than one arc. Thus, while K seems relevant for the S-graph, C is relevant for the L-graph, since the logical structure of (130a) must represent the fact that

7.6. OVERLAY ARCS AND CLAUSE STRUCTURE

265

it is the complement clause which functions as logical object of the predi­ cate corresponding to said. The closure arc which erases C permits all of these desirable conditions to be maintained. We see later that closure arcs play a similar role with respect to prepositional and postpositional phrases which, in our terms, have a structure essentially identical to that of complementizer forms. PN laws 54 and 55 claim, in effect, that Overlay arcs are entirely ex­ ternal to the description of basic clause structure. Since the former re­ quires that all organic Overlay arcs be immigrants, and the latter says that the tails of such arcs cannot be inherent, Overlay arcs are never present in the strata of basic clauses, as Theorem 57 in effect shows. This fact justifies the term "Overlay," whose connotations are that the grammatical relations represented by Overlay arcs are an overlay on the "basic" gram­ matical relations which define the correspondents in the interpretation of basic clause constituents. Further, these laws justify the intuition that Overlay phenomena are less central than, e.g., those involving Term arcs, Oblique arcs, etc., as far as clause structure is concerned. For the only Overlay arcs with no predecessors are replacers, which must have samesign local sponsors, that is, Overlay sponsors. If these. Overlay sponsors are not themselves replacers, they must be immigrants. Thus, the sponsor chains into which Overlay arcs enter must begin with nonOverlay arc pred­ ecessors, including Central arc predecessors. Another way to put the above is that it is conceivable that languages could exist whose PNs contained no Overlay arcs. But current laws pre­ clude the possibility of any languages without Central (in fact, Term) arcs. In this sense too, Central arcs are more central than Overlay arcs. One of the first major ideas of stage 1 RG was that there is a basic distinction between phenomena like passivization, raising, etc., which in­ volve Term relations, and those like topicalization, relativization, etc., which do not. This distinction is, in effect, represented in APG by the subdivision of Nominal arcs into Central arcs and Overlay arcs. An exten­ sion of the contrast is given in Chapter 12, where the two subsets of

266

7. FOCUS ON CLAUSE STRUCTURE

Nominal arcs are seen to contrast as far as linear ordering is concerned (see the discussion of Shallow arcs). We can now explore the possibility of further characterizing Overlay arcs and distinguishing their properties from those of Central arcs. One productive way to do this is to inquire into the way Overlay arcs enter into successor/predecessor pairs. We have seen that, e.g., Term arcs can be both predecessors and successors while, e.g., domestic Oblique arcs can be predecessors but never successors. Domestic Cho arcs and Organ­ ic Dead arcs, as discussed in the following chapter, can only be successors. In most cases, the predecessor of an Overlay arc is a Central arc, as in, e.g., (130). This could be taken as a law. However, certain facts seem to preclude a claim of this generality. In certain cases, it seems necessary to recognize Marq arcs, which play a central role in our treat­ ment of nominal flagging, as predecessors, e.g., in stranded preposition situations like: (131) John, I wrote to yesterday. These are discussed in Chapter 13, section 4. Also, in some cases, it may be necessary to allow P arc predecessors for at least some types of Overlay arcs. We do not, however, count English examples of the type in (132a,b) as instances of this: (132) a. Intelligent, Tommy isn't. b. Fond of Mary, no one could really be. At first glance, these might seem to involve topicalization of predicates. But, as forms like (132b) show, something else is involved, for the "object" of the predicate itself is also affected. In our terms, these cases involve Top arcs with Cho arc predecessors, the Cho arcs being a function of the raising out of the complement of the auxiliary be. The same point holds for cases where predicate nominals function as topics, as in;

7.6. OVERLAY ARCS AND CLAUSE STRUCTURE

267

(133) A good doctor, no one ever claimed Schwarzheim to be. Recall that our analysis of predicate nominals takes them to be heads of P arc local successors. In spite of this, we deny that it is the P arc which is a predecessor of the Top arc in cases like (133). Again, we take be to be an auxiliary verb triggering raising, which leads to its initial 2

arc having a Cho arc successor. It is the Cho arc that is the predecessor of the Top arc. Ignoring the structure relevant to the fact that claimed in (133) is a raising trigger and that Schwarzheim is the head of an immigrant 2 arc in the claimed clause, the relevant structure of (133) would be:

GRx

no one

(ever) claimed Cho Top

a good doctor

a

Here B, the Cho arc determined by the immigrant C, is the predecessor of the Top arc. Hence cases like (132) and (133) do not show that English allows P arcs to be predecessors of Top arcs. In spite of this, there are probably

268

7. FOCUS ON CLAUSE STRUCTURE

languages which permit this, in particular, so-called VSO languages where one speaks of topicalizing verbs. Breton is such a case, as discussed in Anderson and Chung(1977). In particular, their example (42b) would seem to preclude any treatment of verb topicalization in terms of Cho arc pred­ ecessors for Top arcs, along the lines of our treatment of (133) in (134). This phenomenon in Breton is discussed in greater detail in Wojcik (1976), who concludes that there is a "verb fronting" rule in Breton. This trans­ lates in our terms as a construction in which P arcs have Overlay succes­ sors. We conclude that in addition to Central arc predecessors and Marq arc predecessors, Overlay arcs may on occasion have P arc predecessors. Further, it is likely that in some cases, e.g., in languages permitting sen­ tences like "Whose did you see book," it will be necessary to allow Gen arc predecessors for Overlay arcs. Thus, at the moment, no very elegant or restrictive characterization of Overlay arc predecessors is in general available. One of the early RG ideas was that while phenomena like passivization, raising, inversion, antipassivization, etc., could feed and bleed those like relativization, topicalization, and questioning, the converse is never possi­ ble. Informally, one can, e.g., topicalize a 1 created by passivization, but there are no cases of turning a topic into a 1. Translating into APG terms, what is involved are constraints on the possible successors of Overlay arcs. In particular, while Central arcs can be predecessors of Overlay arcs, Overlay arcs can never have Central arc successors. This negative remark, even if true, does not adequately characterize the class of possible successors of Overlay arcs. This class seems highly restrict­ ed. One might even be led to suggest that the class in question is null: (135) Overlay arc (A) -» Not ((3B) (Successor (B, A))) . Principle (135) makes what amounts to a claim about an issue which has divided transformational grammarians. Expressed in transformational terms, it involves the question of whether so-called unbounded movement phenomena are to be treated by a succession of bounded movements, or by a single unbounded movement. Consider:

7.6. OVERLAY ARCS AND CLAUSE STRUCTURE

269

(136) Who do you think Bob said I liked? Here who is understood as the 2 of liked. The question in transformation­ al terms is whether it achieves its position by moving once from its origi­ nal position to its final locus or whether it moves successively, first to the complementizer of I liked, then to the complementizer of the next clause, etc. For discussion, see Chomsky (1977) and references therein. In APG terms, the analogues of the so-called movements are successor arcs. Thus, the alternatives reduce in our terms to whether the 2 arc of the liked clause headed by who has a single Overlay successor arc, say a QU arc, whose tail corresponds to the complementizer constituent of the whole sentence, or whether the 2 arc has a QU successor corresponding to the complementizer of / liked, with that QU arc having itself a QU arc successor in a higher complementizer, etc. But (135) claims that only the former analysis is possible, since the latter involves providing an Overlay arc with a successor. There is to our knowledge no serious evidence from well-known lan­ guages indicating that Overlay arcs ever have successors. Hence, it would be natural to accept the strong and restrictive claim in (135) as valid. However, regardless of the situation in languages like English, recent data about Afrikaans made available by du Plessis (1977) seems to indicate fairly unequivocally that some Overlay arcs do have successors. Writing in a transformational framework, du Plessis shows, on the basis of the possibility of leaving prepositions in "intermediate" positions, that question forms move successively in Afrikaans. In APG terms, his data can only be interpreted as indicating that some QU arcs have successors. However, while this Afrikaans data apparently precludes accepting (135) as a PN law, it does not preclude the possibility of still narrowly restricting successors of Overlay arcs. One can allow for the Afrikaans type data and still represent the insights of RG discussed just above (135) by imposing: (137) PN Law 56 (The Overlay Arc Successor Law) Overlay arc (B) Λ Successor (A, Β) -> Same-Sign(A 1 B) .

7 . FOCUS ON CLAUSE STRUCTURE

270

This allows a QU arc to have a QU arc successor, as in the Afrikaans cases discussed by du Plessis. But it precludes the possibility of one type of Overlay arc being the successor of a distinct type. More important­ ly, it yields a theorem which accounts for the RG observations that topicalization, relativization, etc., do not "feed" passivization and similar phenomena reconstructed in APG terms with Term arcs: (138) THEOREM 59 (The Overlay Arc Successor Theorem) Overlay arc (A) Λ Central arc (B) -> Not (Successor (B, A)) . Proof. Immediate from PN law 56, given that the classes of Central

R-signs and Overlay R-signs are disjoint, and hence so are the arc class­ es these define. QED. Thus, although (135) seems too strong, one can still tightly constrain possible successors of Overlay arcs to preclude the possibility that these arcs could enter into the description of Central arcs or basic clauses. Recall that the successor relation organizes arcs into chains, whose first members are entrant arcs and whose final members are called egressors in Chapter 14. If (135) were valid, every Overlay arc would be an egressor. Since it is not, this is not quite the case. However, if PN law 56 holds, Overlay arcs still have a unique role in successor chains. Even when an Overlay arc is not the last member of a chain of successors, all following arcs have identical R-signs. In terms of the interpretation of the formalism, once a nominal comes to bear an Overlay grammatical relation, it can not bear a distinct successive relation, although it can bear the same Overlay relation to a distinct linguistic element (necessarily a "higher" one, given PN law 51). PN law 56 represents the major constraint we currently feel capable of imposing on Overlay arcs. One further observation, however, involves the class of arcs which Overlay arcs can assassinate. We know of only two sorts of cases in which Overlay arcs need be taken as assassins. First, commonly, Overlay arcs assassinate their predecessors under The Successor

7.6. OVERLAY ARCS AND CLAUSE STRUCTURE

271

Erase Law. Hence, given the nature of predecessors, in these cases an Overlay arc assassinates an arc which sponsors it. Second, and so far attested to our knowledge only in the situations discussed by du Plessis (1977) where QU arcs sponsor copy arcs (see Chapter 11 for this concept), an Overlay arc which is a copy arc replacer assassinates the arc it re­ places under The Replacer Erase Law. But given the definition of "Replace", in this case also the assassin is erasing an arc which spon­ sors it. The following generalization then apparently governs assassina­ tion by Overlay arcs: (139) PN Law 57 (The Overlay Arc Assassin Law) Overlay arc (A)

Λ

Assassinate (A, B) -> Sponsor (B, A) .

This completes the present discussion of Overlay arcs, although we return to this topic briefly in Chapter 13. The central thrust of this dis­ cussion is that the domain of Overlay arcs is external to basic clauses and represents a realm of structure "superimposed" on basic clauses. In particular, Overlay arcs can never be neighbors of any Central arcs. Fur­ ther, Overlay arcs are claimed to be tightly restricted with respect to their successors and the kind of arcs they can assassinate, as specified in PN laws 56 and 57.

CHAPTER 8 CHO ARCS 8.1. The temporary Chomeur condition The notion Chomeur is one of the distinctive elements of both RG and APG, and a concept largely without antecedents in previous linguistic work.1 Cho arcs, which formalize this concept in the present framework, are subject to a number of restrictive conditions separating them from other arcs. Informally, one can characterize Cho arcs as follows. Each Cho arc is either domestic or a graft. Graft Cho arcs are replacers, and locally sponsored by domestic Cho arcs. We essentially ignore graft Cho arcs in what follows since they follow the laws for grafts and are not otherwise notable. Domestic Cho arcs are necessarily local successors of Term arcs. This means, inter alia, that Cho arcs (i) cannot be elements of L-graphs and (ii) cannot have the coordinate C1 (see Theorem 62, The

1 There are some vague precursors of analyses involving chomeurs for special types of constructions, usually passives, to be found in the writings of various traditional grammarians. Jespersen's (1924: 164) concept of the "converted sub­ ject" of a passive fits into this category as does, perhaps, his use of the symbolization "S g " (see e.g. Jespersen[l937: 26] for the "initial" subject of a passive clause). A similar precursor is also found in the French grammatical tradition which refers to this nominal as "complement du passif" or "complement d'agent" (see Grevisse [l969: 56l], who remarks "et Ie sujet du verbe actif devient Ie com­ plement d'agent du verbe passif..."). Tesniere (1959: 109) speaks of this nominal as the contresujet but identifies it with his second actant, a concept which refers to the direct object in an active clause. In these works, one senses a fairly clear perception that the nominal corresponding to the subject of an active has some special status in passives distinct (except for Tesniere) from any status found in actives. Missing, beyond any formal theory of such ideas, is a perception of the generality of the relevant chomeur concept, its relevance to many clause types having nothing to do with passives.

8.1. THE TEMPORARY CHOMEUR CONDITION

273

Cho Arc Nonself-Sponsoring Theorem, and Theorem 77, The Cho Arc Nonlogical Arc Theorem, below). Our informal intention is that, although the chomeur relation is a primi­ tive relation like 1, 2, etc., the distribution of Cho arcs in PNs is de­ termined by independent factors. Thus, informally, Cho arcs exist in all and only those contexts where universally specifiable conditions force them to exist. If, as claimed, all Cho arc distribution is determined by universal principles, it might be asked whether it is not possible to dispense entire­ ly with a primitive chomeur relation. We have grappled with this problem, but our attempts to construct a theory which recognizes no such relation have not been satisfactory. We therefore leave it as a problem for others to attempt to construct such a desirable (from an Occam's Razor point of view) theory. We point out in Chapter 14, section 7, after discussing our rule formalism, some reasons why Cho arcs seem indispensable. The idea behind the chomeur relation has always been that the exist­ ence of this permitted clause structures to remain consistent with Term arc stratal uniqueness, given that both (i) there is a condition of coordinate fall-through (see PN law 26, The Fall-Through Law) or its analogue in RG and (ii) facsimile Term arcs can coexist in single clauses. For it seems (but see section 2 below) that, under these conditions, only a chomeur re­ lation prevents clauses from violating stratal uniqueness. For example, consider a partial (Cho arc-free) representation of a passive clause like: (1) The swill was lapped up by Ted.

Ted

the swill

(was) lapped up

274

8. CHO ARCS

Since there is a motivated C2 stratum in (2), it follows from The FallThrough Law that the coordinate sequence of A in (2) must contain coordinate C2 , violating stratal uniqueness, unless there is some arc in the C2 stratum which locally assassinates A. The existence of Cho arcs permits this, since the correct structure for (1) involves in addition a Cho arc as local successor and assassin of A (see Theorem 66, The Cho Arc Predecessor Local Assassination Theorem, which proves that Cho arcs invariably locally assassinate their predecessors). This Cho arc prevents A from falling through to C2 and thus preserves stratal uniqueness. Translated into the terms of the present work, the discussion of (2) illustrates what have, within RG, been assumed to be the necessary and sufficient conditions for the existence of a Cho ate in a structure. This "traditional" view of chomeurhood, represented, e.g., in stage 1 RG terms by the statement in Chung (1976a) and in stage 2 terms by the statement in Perlmutter and Postal (1977),2 needs clarification. It turns out to be over­ simplified. To help clarify the situation, the following terminology is of great value: (3) a. Def. 136: O u t f l a n k ( A r B ) «-» Facsimile (Α, Β) b. Def. 137: O v e r r u n ( Α , Β ) «-» Outflank (Α, Β)

λ

λ

c

^(B)

λ (A) .

Term arc(A) .

That is, A outflanks B if and only if A and B are neighbors, have the same R-sign, and the first coordinate index of A is +1 of some coordinate index of B. A overruns B if and only if A outflanks B, and A is a Term arc (and, hence, so is B). It can be seen that in (2) B overruns A . The RG idea about chomeurhood can then be roughly ex­ pressed in present terms as follows, bearing in mind that RG had no notion Successor and thus that a really accurate translation into present terms is not possible: 2

The reader is advised to ignore the formulation in Postal(1977) which, be­ yond the limitations of nonAPG formulation, involves some errors.

8.1. THE TEMPORARY CHOMEUR CONDITION

275

(4) The RG Chomeur Condition "Translated" into PN Terms (3A)(0verrun (A,B)) -> (3C)(Local Successor(C1B)ACho arc (C)). Evidently, (4) correctly predicts that A in (2) must be the predecessor of a parallel Cho arc. (4) is essentially right for a wide range of cases, in­ cluding almost all those considered in RG. RG also incorporated a principle, called The Motivated Chomage Law, which said, in effect, that Cho arcs exist only when determined by (4). As noted in Perlmutter and Postal (1977), The Motivated Chomage Law can be formalized by making the "traditional" Chomeur Condition a biconditional, yielding: (5) The RG Chomeur Condition and Motivated Chomage Law "Translated" into PN Terms (3A)(0verrun (A,B)) «-» (3C)(Local Successor(C,B) ACho arc (C)). This says that an overrun arc must be the local predecessor of a Cho arc and, conversely, a Cho arc predecessor must be an overrun arc. (5) not only specifies conditions under which Cho arcs "save" PNs from stratal uniqueness violations, but claims that Cho arcs can only occur under such "saving" conditions. It excludes the possibility, advocated by such writers as Comrie (1977), Jain (1977), and Keenan (1975), of so-called "spontaneous demotion." In APG terms, the latter is precisely the exist­ ence of (domestic) Cho arcs in contexts distinct from those specified in (4). "Spontaneous demotion" has typically been advocated as a description of so-called impersonal passive clauses, like the following in Welsh (see Bowen and Jones [I960]). (6) gwelir

hi

see—Impersonal her/she = she was seen. In such cases, there is no reason in Welsh to take the nominal hi, which is the initial 2, to bear the 1 relation in the clause. Impersonal verbs like gwelir do not agree, although verbs in Welsh normally agree with their

276

8. CHO ARCS

final Is . Hence, it seems initially plausible to describe such sentences, which can contain a surface chomeur nominal as well, e.g.: (7) gwelir hi gan yr athro by

the teacher = "She was seen by the teacher."

as simply involving a structure in which the initial 1 arc is succeeded by a Cho arc, although it is not overrun. This would yield for (7), in PN terms, a structure like the following:

Cho/c.

(gan) yr othro

hi

gwelir

This structure of course violates (5) (though not (4), because the antece­ dent condition of (4) is not met in (8)), since it has a Cho arc successor of a 1 arc which is not overrun. Hence "spontaneous demotion" is incom­ patible with The Motivated Chomage Law. We do not believe that there is any "spontaneous demotion," and ultimately propose a PN law which in­ corporates the Motivated Chomage Law. Consequently, it is incumbent upon anyone who accepts the present theory to argue that "sponteneous demotion" is not the correct analysis of any attested cases, in particular, not those like (6) and (7). This task is, we believe, not difficult to accom­ plish. But we will not be able to deal with it here, contenting ourselves with clarifying the problem. The issue is discussed in Perlmutter and Postal (to appear c). See also note 5 of Chapter 10. As indicated earlier, although (5) is an APG reconstruction of the essential claims of the RG Chomeur Condition and Motivated Chomage Law, we do not regard (5) as adequate. Our claim is that the class of contexts determining Cho arcs is smaller, in formally specifiable ways, than the class picked out merely by the overrun condition. We assume overrunning

8.1. THE TEMPORARY CHOMEUR CONDITION

277

to be a necessary condition for determining Cho arcs but not sufficient. The overrun condition (more exactly, a slight further specification of it) is only one of two conditions which are jointly necessary and sufficient. The need for the second condition, one involving the existence of an erase relation between the overrunning arcs, is illustrated by examples such as: (9) a. John tickled himself. b. German Solche Sachen sagen sich nicht. Such

things say

self not = "Such things are not said.'

which have the following respective structures: (10) a.

John

himself

tickled

b.

P \C|C2

sagen (nicht)

solche Saehen sich

In these structures 3 there are overrun arcs which do not sponsor Cho arcs, and, where, in contrast to, e.g., (2) and (7), this is the desired result. For —

O corresponds to surface elements like French on and German man. Although more restricted in reference than UN, which we take to be totally unspecific,

278

8. CHO ARCS

instance, in (10a), C overruns B and in (10b), D overruns C. In neither case does the overrun arc sponsor a Cho arc, nor would one wish that it did. Thus, in cases where an arc sponsors a "pronominal" arc, either of the "coreferential" variety, as in (10a), or the "copy" variety, as in (IOb),4 no Cho arcs are, or should be, present. These are both structures where replacers overrun the replacees. But replacees should never have Cho aic successors (see Theorem 70, The Replacee Employed Successor Theorem, below). This is the first illustration that a mere overrun condition is not suffi­ cient to state the desired PN law governing Cho arc distribution. These cases are easily dealt with by observing that situations like (2), where overrun correctly determines Cho arc necessity, contrast with those like (10), where overrun must not yield Cho arcs, in an obvious formal way. In (10), the overrunning arcs erase the arcs they overrun, while this is not the case in (2). We claim that this is no accident and that a proper con­ straint on Cho arc occurrence in cases where A overruns B is: (11) Not (Erase (A, B)) . This condition not only eliminates from relevance in our terms all cases where the overrunning arc is a "pronominal" arc, as in (10), but also cases where the overrunning arc is a "closure," as discussed in Chapter 13. That is, it eliminates all cases where an overrunning arc is a replacer. Thus, there are two major classes of overrunners: (i) nonreplacers and (ii) replacers. To further illustrate, (11) also properly prevents Cho arcs in cases like (12) a. Sally sent cookies to Louise.

nodes labeled O like those labeled UN belong to the set of nominal nodes

Inexplicit discussed in detail in Chapter 9. These nodes have special properties, in particular, the possibility of heading arcs with a greater freedom of being than other Nominal arcs.

zeroed

^These notions are defined precisely and discussed in detail in Chapter 11.

279

8.1. THE TEMPORARY CHOMEUR CONDITION

b.

sent

Marq Sally

cookies

Louise

Here C is a cosponsored graft (replacer), of the closure arc type, which overruns and erases D . No Cho arc is possible here and this is properly determined by (11), since D is erased by the arc which overruns it, C. Crucially, arcs in Overrun are necessarily D-Neighbors,5 and, hence, any overrun arc which is erased by its overrunner is necessarily locally assassinated, and so will not fall through into the first stratum "occupied" by its overrunner. From an extratheoretical point of view, it is understandable why Cho arcs exist in cases like (2), but not in those like (10a,b) and (12b). This makes sense in the context of the view that the rationale for Cho arcs is to "save" structures from stratal uniqueness violations. For, although all of (10a,b) and (12b) involve overrun arcs, in no case is there a viola­ tion of stratal uniqueness. This follows because in each case the overrun arc is assassinated by an arc in the first stratum containing the overrun­ ning arc. The Fall-Through Law does not permit the overrun arc to fall through into that stratum, and no stratal uniqueness violation ensues. This observation is a clue to an inadequacy of RG formulations of The Chomeur Condition, like (4) and (5). These assumed, in effect, that stratal uniqueness violations would result from any instance of overrun­ ning. But in present terms this is not so. Therefore, we can maintain the

5 Arcs in Overrun are necessarily distinct, since if A overruns B, the first coordinate of A is +1 of some coordinate of B, impossible if A = B.

280

8. CHO ARCS

"traditional" pretheoretical conception of the rationale for the chomeur relation while postulating a weaker principle of Cho arc determination. It is at best necessary to determine the presence of Cho arcs in cases where nothing otherwise prevents the overrun arc from falling through into the stratum of the arc which overruns it. 6 For the principles of coordinate determination of Chapter 6 guarantee that in cases like (10) and (12b) no stratal uniqueness violations can develop. The Replacer Erase Law and The Fall-Through Law insure that if one arc replaces another, they can never co-occur in the same stratum. Condition (11) as a constraint on the distribution of Cho arcs properly excludes from relevance a class of cases including "pronominal" arcs and closures which were never considered in RG, because that framework had no account of structures described in terms of the APG concept Re­ place. We now turn to cases which fall under (11) and which were dealt with in RG. Consider a so-called "short" passive clause like: (13) Melvin was pushed. In RG terms, such a clause would have been analyzed as having a special type of nominal as its initial 1, one we have earlier represented as UN (see Chapter 9). This nominal would then be a chomeur in (13), just as ordinary nominals like Mary, the former king, etc., are chomeurs in stan­ dard "long" passives. Moreover, some provision must be made for the fact that the nominal in question in (13) is not a part of the S-graph of the clause. In APG terms, this would mean that the relevant Cho arc would self-erase. Thus, in our terms, the "traditional" relational analysis of (13) would yield the overall structure:

6 We see below that this class of cases is coextensive with those where no employed arc locally erases the overrun arc.

8.1. THE TEMPORARY CHOMEUR CONDITION

281

Cho

twos) pushed UN Melvin

However, there are reasons to doubt the validity of a structure exactly like (14). First, "short" passives are found in almost every language having passives. 7 Indeed, it is traditional wisdom that there is a strong implicational relation such that languages with "long" passives have "short" passives, but not necessarily conversely.8 But, although many languages have stranded prepositional flags of various kinds, no attested language has, to our knowledge, a stranded flag in "short" passives. We know of no language with the analogue of: (15) *Melvin was pushed by = "Melvin was pushed by unspecified." It seems then that this is not an idiosyncracy of English but a general fact about "short" passives which should receive some principled basis in an adequate theory (a point stressed to us early on by G. K. Pullum). Structures like (14) offer no obvious basis for such an explanation. Second, and more importantly (see Chapter 9), UN in (14) occurs as the head of two distinct arcs. This is, however, incompatible with an interesting constraint which, we argue in Chapter 9, can be placed on the unique nominal UN , a constraint with important, otherwise correct empiri­ cal predictions. This constraint, PN law 79, The UN Node-Headed Arc

7

J. Lawler of the University of Michigan has informed us that in Achenese, a language of Indonesia (see Lawler [l977]), this condition may not be met. Although Achenese has ubiquitous long passives, it is not clear it has any short passives. O

Jespersen (1924: 167-68) noted, for example, that some languages only allowed short passives. More recently, the idea that short passives are fundamental to passivization has been expressed more precisely in different ways by Langacker and Munro(1975) and Eckman (1974).

282

8. CHO ARCS

Limitation Law, is the chief current motivation for our rejection of struc­ tures like (14). Finally, there is no positive evidence that the initial 1 arc of a clause like (13) sponsors a Cho arc. No rule of English or any other language with an analogue of (13) seems to require that the nominal in question occur on a Cho arc. These considerations raise the possibility that there is an analysis of short passive examples like (13) which would avoid any Cho arc. Of course, there is no such analysis if one adopts the RG Chomeur Condition in (4), since A in (14) is overrun by B. This then also suggests that a condi­ tion weaker than (4) is required. Our proposal is that the correct structure for (13) is not (14) but (as indicated without discussion in Chapter 6):

(16)

UN

Melvin

(was) pushed

In (16), A is locally assassinated by B, which overruns it, and hence condition (11) is not met. The Fall-Through Law guarantees that A does not fall through to C2 . Thus, although A is not erased by a Cho arc, no violation of stratal uniqueness can ensue. Structures like (16) have the following other virtues. They provide a basis for an account of why no stranded Cho flag is possible in (13) or any analogous case (if assigned structures parallel to (16)), since obvious­ ly Cho flags are impossible if there is no Cho arc.9 Secondly, (16) does g

It remains to show that examples like (15) could not be described in terms of flagging of erased 1 arcs like A in (16). This is in fact impossible, given the

8.1. THE TEMPORARY CHOMEUR CONDITION

283

not require UN to occur as the head of more than one arc, which is signifi­ cant, as shown in Chapter 9. This is the major motivation for structures like (16). It predicts, correctly, that no known rule treats UN in such cases as the head of a Cho arc. Further, although it is not possible to discuss rules at this point, structures like (16) require no more rules than (14). Finally, (16) is a simpler structure than (14), having one less arc, one less sponsor pair and one less erase pair (see B, Sponsor (B, A) and Erase(B 1 B) in (14)). Hence, ceteris paribus, (16) is to be preferred. We claim that APG theory can be made sufficiently restrictive so that the pair Erase (B, A) in structures like (16) is a function of principles of APG uni­ versal grammar (see Theorem 68 below). The minimal change in (5) consistent with these considerations would assume that the excessive strength of RG formulations of Cho arc distribu­ tion is completely characterized by (11). One could assume that the class of cases where an arc A overrun by an arc B need not have a Cho arc successor involves structures where B erases A. Of course, such situa­ tions are not limited to passivization. We would also recognize similar erasure of an overrun arc by the arc which overruns it in many other cases. For example, consider: (17) a. Melvin teaches algebra to children. b. Melvin teaches children algebra. c. *Melvin teaches to children. d. Melvin teaches children. We take such examples to indicate that clauses headed by teach involve initial 2 and 3 arcs and that in such clauses the 3 arc of a ditransitive clause can sponsor a successor 2 arc. Hence we would analyze (17b) as:

conception of nominal flagging sketched in Chapter 13. The reason is that, in that theory, presence of a flag requires that the flagged nominal head an arc with a successor. Given erasure like that in (16), this involves a violation of The Unique Eraser Law.

284

8. CHO ARCS

(18)

vwww*"

Melvin

children

algebra

leaches

On the other hand, (17a) does not involve the successor arcs in (18) and is thus a single stratum structure in which children is a final as well as initial 3 , algebra a final as well as initial 2 . What of (17d)P We take this to involve the same phenomenon relevant for (18), a 3 arc locally sponsoring a 2 arc successor. However, the initial 2 of (17d) is UN , and we claim that the 2 arc headed by UN is zeroed by the overrunning 2 arc (sponsored by the 3 arc) rather than by a Cho arc. The structure of (17d) would be: (19)

ΛΜΛΛΛ

Melvin

children

UN

teaches

Our analysis does not offer any insight into the ill-formedness of (17c), otherwise parallel to (17a). This is not a general feature of verbs in clauses involving so-called 3-2 advancement, as shown by: (20) a. Melvin writes (letters) to movie stars. b. Melvin sings (pornographic songs) to nuns. It must apparently be regarded as an ad hoc restriction making 3-2 ad­ vancement structures effectively necessary with teach when the initial 2

8.1. THE TEMPORARY CHOMEUR CONDITION

285

is UN. Other 3-2 advancement verbs, e.g., t e l l , do not permit an initial UN 2 at all: (21) a. Melvin tells stories to trolls. b. Melvin tells trolls stories. c. *Melvin tells to trolls. d. *Melvin tells trolls. or else, like s h i p , permit an initial UN 2 only if the initial 3 arc does not have a 2 arc successor: (22) a. We ship meatballs to retailers. b. We ship retailers meatballs. c. We ship to retailers. d. *We ship retailers (*on the analysis where retailers is the head of a 3 arc). Obviously, there is considerable idiosyncratic behavior associated with UN-headed 2 arcs in initially ditransitive clauses in English. A further case where an overrunning arc erases the arc it overruns is provided by antipassive constructions (discussed briefly in Chapter 7) as analyzed in Postal (1977). In such cases, 1 arcs of transitive clauses have 2 arc successors, normally leading to a Cho arc successor for the initial 2 arc. In Postal (1977) it is argued that French unspecified object clauses like: (23) Pierre a mange Pierre has eaten = "Pierre has eaten, ate" involve antipassivization. In that paper, it was assumed that the initial 2 nominal, UN , was the head of a Cho arc. But, in present terms, we pro­ pose the following analysis for (23):

286

8. CHO ARCS

(24)

Pierre

(α) mange UN

There are thus a variety of cases analyzed in APG terms as involving erasure of an overrun arc by the arc which overruns it rather than by some other, overlapping arc. However, the reader may have noticed a peculiar kind of complementarity in cases we have and have not analyzed as in­ volving this kind of erasure. Whenever zeroing of one overrun arc by a nonoverlapping arc was posited, the head of the zeroed arc has been UN or O (more precisely, a nonterminal node-labeled UN or 0), while no ex­ amples were provided of, e.g., cases of UN-labeled nodes heading Cho arcs. This complementarity is no accident. Our claim is that only a tiny handful of nominals can head arcs subject to the kind of zeroing illustrated in, e.g., (24). UN is the major example of this set. At the same time, UN can never, we claim (see Chapter 9), be the head of a Cho arc. Involved in examples like (24) are instantiations of the following pattern: (25) (3A)(3B) (Zeroes (A, B) a Not (Sponsor (Β, A)) a Nominal arc (B)) . Our claim is that this pattern is only possible when the head of B is one of the limited set of elements referred to above (see PN law 76 of Chapter 9). Most nominals, e.g., Mary, the creature under the bed, the fact that it is raining, bran and soy flour, the king, who is a homosexual, etc., are excluded. It is for this reason that, e.g., "short" passives like (13), "short" antipassive clauses like French (23), "short" 3-2 advancement clauses like (17d), etc., always involve invisible nominals with an extreme­ ly limited range of interpretations. We return to this matter in Chapter 9.

287

8.1. THE TEMPORARY CHOMEUR CONDITION

We are ready to further formalize a reconstruction of the RG principles involved in the Chomeur Condition and The Motivated Chomage Law, weakened, as discussed above, to allow analyses like (16), (19), and (24). Before stating this, it is useful to introduce a further defined concept, only trivially different from Overrun, namely, c^-Overrun (A, B ) (read "A overruns

B

at

Cj c ")-

Thissimplypicksouttheparticularcoordinateof

the stratum where the overrunning arc first appears: (26) Def. 138: C j c -Overrun (A, B) Overrun (A, B)

A < CJ I β > (A)

.

Given (26) plus our comments about the role of erasure and the possi­ bility of analyses like those in (16), (19), and (24), the "traditional" Chomeur Condition can be further amended as follows: (27) (3A) (CJf-Overrun(AjB) Λ Not (Erase (A,B))) -» (3C)(Cho arc (C)

Λ

Successor (C,B)) . (27) says an overrun arc, B , must have a Cho arc successor if the arc which overruns it does not erase it. (27), unlike (4), requires only that the Cho arc be a successor of B , not a local successor. In fact, in all cases the Cho arc in question is a local successor. However, one need not specify this in (27) since it is a consequence of independent assump­ tions (see Theorem 63 below). (27) is largely a reconstruction and modification in present terms of the "traditional" Chomeur Condition. But it does not incorporate the "traditional" Motivated Chomage Law. (27) specifies that under certain conditions, those in its antecedent, Cho arcs are required. It in no way precludes the occurrence of Cho arcs under circumstances distinct from those in the antecedent. Since we believe that nongraft10 Cho arcs are precluded under circumstances distinct from those in the antecedent of (27), we incorporate a corresponding statement in the theory:

^Graft Cho arcs are coextensive with Cho arc replacers, as shown by Tiieorem 100 in Chapter 10.

288

8. CHO ARCS

(28)

(3C)(Cho arc (C) a < c k β > (C) λ Successor (C, B)) (ΉΑ) (Cjc -Overrun (Α, Β) λ Not (Erase (A, B))) .

However, (28) simply involves taking the consequent of (27) as antecedent and the antecedent of (27) as consequent. Thus, consistent with the earlier observation that The Motivated Chomage Law can be incorporated in a "relational" theory by strengthening the Chomeur Condition to a bi­ conditional, one arrives at a single biconditional principle, which makes strong claims about the distribution of all nongraft Cho arcs: (29) The Temporary Chomeur Condition (ΉΑ) (Cjc -Overrun (Α, Β)λ Not (Erase (A, B)) «-* (3C)(Cho arc (C) λ

< c k β > (C) λ Successor (C, B)) . From left to right, (29) states that if an overrunning arc does not erase the arc it overruns, there must exist a Cho arc successor of the overrun arc (which will, by Theorem 66, The Cho Arc Predecessor Local Assassina­ tion Theorem, proved below, locally assassinate the overrun arc). The Fall-Through Law will then keep the overrun arc out of stratum Cj i . Thus, (29) states that in all cases of Overrun, there is a binary division of possi­ bilities. Either the overrun arc is erased by the arc which overruns it, or the overrun arc sponsors a Cho arc successor. Although The Temporary Chomeur Condition determines in all cases of Overrun the division of possibilities just mentioned (this will be weakened in the next section), it says nothing about what kinds of nominals can/must be treated in one way and what kinds in the other. But, as already men­ tioned, only a very small set of overrun arcs, including those whose heads are labeled UN , can be erased by nonreplacer arcs which overrun them. On the contrary, such arcs cannot be succeeded by Cho arcs. The conse­ quence is that so far APG not only properly allows, e.g., the analysis in (30) and (31), it also unfortunately allows the formally parallel structures where the elements UN and Mary are interchanged:

8.1. THE TEMPORARY CHOMEUR CONDITION

UlM

UWC

289

(was) tickled

(31)

Mary Joe

(was) f ick led

We return in Chapter 9 to the problem of excluding such evidentally illegal cases, like those where UN and Mary are interchanged.

8.2. Cosponsorship of domestic Cho arcs We turn to an aspect of our theory of Cho arcs which has been largely ignored up to this point, although it was touched on in Chapter 5. This is the claim that every domestic Cho arc has two sponsors. We now clarify and formalize the view that domestic Cho arcs are cosponsored. First, recall from Chapter 5 The Employed Domestic Arc Theorem: (32) THEOREM 38 (The Employed Domestic Arc Theorem)

Employed(A) Λ Domestic (A) Λ Sponsor (Β,Α) Λ Sponsor (C,A) -» B = C . Obviously, (32) would make no sense unless the equivalent principle with­

out the first conjunct failed to hold for Cho arcs. Without this, one could simply specify that all domestic arcs have unique sponsors. Implicit in Theorem 38 is the view that domestic Cho arcs have more than one spon­ sor (two sponsors to be consistent with The Maximal Two Sponsor Law).

8. CHO ARCS

290

The informal motivation for this position is as follows. Our pretheoretical interpretation of the Sponsor relation was that the sponsoring arc is a necessary condition for the existence of the sponsored arc. Given The Temporary Chomeur Condition, a domestic Cho arc can exist only if, in addition to its predecessor, there exists an arc which overruns that predecessor. Hence, the overrunner is a necessary condition for the exist­ ence of the Cho arc, just as its predecessor sponsor is. It is thus consis­ tent with the interpretation to assume that the overrunning arc is the second sponsor of a domestic Cho arc. Recall the clause represented in (18) above:

Cho 1

Melvin

chi Idren

algebra

teaches

Here it is the sponsor relation between C and D which is at issue. To guarantee that domestic Cho arcs have the relevant extra sponsor, we state first: (34) PN Law 60 (The Cho Arc Cosponsor Law) Cho arc(A) -» (3B)(3C)(Cosponsor(C, B, A)) . This simply says that every Cho arc has two sponsors,11 and thus pre­ cludes representations like (33) minus the pair Sponsor (C, D). While (34)

11 This PN law need not, under present assumptions, be restricted to domestic Cho arcs, since Cho arc grafts are, as noted in the previous note, replacers. But replacers have two sponsors by definition. Thus a typical Cho arc graft would be the closure (see Chapter 13 for this concept) A in (i), which would be the repre­ sentation for the italicized phrase in (ii):

8.2. COSPONSORSHIP OF DOMESTIC CHO ARCS

291

is consistent with (33), it does not suffice to guarantee that (33) is correct, since there is nothing in (34) which identifies the particular arc distinct from the predecessor of a domestic Cho arc which should be its second sponsor. We want this distinct sponsor to be the arc which overruns the predecessor of the Cho arc, i.e., C in (33). Therefore: (35) PN Law 61 (The Cho Arc Second Sponsor Identity Law) Cho arc (A) A Cosponsor (B,C,Α) Λ Successor (A1C) -> Overrun (B,C) . PN law 61 guarantees that the sponsor relation between C and D in (33) is the only second sponsor relation possible. Given PN laws 60 and 61, which, together with The Temporary Chomeur Condition, clarify and deepen the unique status of Cho arcs in the current theory, we are in a position to prove theorems which further highlight this status. First, trivially, any domestic arc with two sponsors is a Cho arc: (36)

THEOREM

60 (The Cosponsored Domestic Arc Theorem)

Cosponsor (A, B, C) Λ Domestic (C) -» Cho arc (C) . Proof. Let C' be a domestic arc with cosponsors A' and B'. If C' is

not a Cho arc, then, since it is domestic, it can have only one sponsor by Theorem 38, The Employed Domestic Arc Theorem, contradicting the ante­ cedent condition of (36). QED.

(0

Cho

Max

by

(ii) Melvin was tickled by Max. Here A is sponsored by both B and C. See Chapter 13, section 2.

292

8. CHO ARCS

More interestingly, there is a demonstrable gap in the intersection of Cho arcs with the arc typology yielding domestic arcs, immigrant arcs, and grafts. At the beginning of this chapter, we noted informally that all Cho arcs were either domestic or grafts. We are now in a position to prove this: (37) THEOREM 61 (The No Immigrant Cho Arc Theorem)

CAoarc(A) -» Not (Immigrant ( A)) . Proof. Suppose, contrary to the theorem, that A' is both a Cho arc and

an immigrant. By the definition of "Immigrant Arc", A' is the (foreign) successor of some arc, B'. Therefore: (i)

Cho arc (A') Λ Sponsor (B', A') .

Hence, by The Cho Arc Cosponsor Law, there is some arc, C', such that: (ii)

Cho arc(A') Λ Cosponsor (B', C', A') Λ Successor (A', B') .

From The Cho Arc Second Sponsor Identity Law, it follows that: (iii) Overrun (C', B') . Thus, Neighbor (C', B') · And, since A' is, by hypothesis, the foreign successor of B', Not (Neighbor (A', B')) and Not (Neighbor (A', C')) · That is, A' has two distinct foreign sponsors. But by PN law 12, The Immi­ grant Local Sponsor Law, A' must have a local sponsor, and hence three sponsors, contradicting The Maximal Two Sponsor Law. QED. Recalling the discussion in Chapter 7 of PN law 49, The No Oblique Successors Law, one can see that Theorem 61 formalizes one property which organic Cho arcs and organic Oblique arcs share. Both must be domestic. However, at this point Oblique arcs and Cho arcs part company. For The No Oblique Successors Law requires all domestic Oblique arcs to be self-sponsoring arcs and hence to have coordinate C 1 . However, do­ mestic Cho arcs cannot be self-sponsoring and so never have coordinate C 1 : (38) THEOREM 62 (The Cho Arc Nonself-Sponsoring Theorem) Cho arc (A) Λ Sponsor (B, A) -> A ^ B .

8.2. COSPONSORSHIP OF DOMESTIC CHO ARCS

293

Proof. Let A' be a Cho arc and suppose Sponsor (B', A') . Contrary to the theorem, suppose that A'= B', Then, by The Self-Sponsor Law, A' has only one sponsor, contradicting The Cho Arc Cosponsor Law. QED. It follows at this point that any organic Cho arc, A , has at least the following properties: (39) a. A has two distinct sponsors, B , C . b. A is not an immigrant arc. c. A is not self-sponsoring (and hence cannot be a C 1 arc). d. If Successor (A, C), then Overrun (B,C) (from PN law 61). However, we have not shown that one can go beyond the conditional state­ ment in (39d) and prove that A is necessarily the successor of an arc. But one can, in fact, prove even more, namely, that there must be some arc of which A is the local successor: (40) THEOREM 63 (The Organic Cho Arc Local Successor Theorem) Organic(A)\ Cho arc (A) -> (ΉΒ) {Local Successor (A, B)) . Proof. Consider an organic Cho arc, A'. From Theorem 61 it follows that A' is domestic. Hence the definition of "Domestic" determines that A' has a parallel sponsor, say B'. From The Cho Arc NonseIf-Sponsoring Theorem, A' ^ B'. Hence, by the definition of "Successor", Successor (A',B'). And since A' and B' are parallel, thus neighbors, Local Successor (A',B'). QED. In Chapter 5 we proved that any arc with a successor has a unique successor (Theorem 14, The Successor Uniqueness Theorem) and claimed that any arc with a predecessor has a unique predecessor. But we did not prove the latter. We are now almost in a position to do so. First, however, we prove the following: (41) THEOREM 64 (The Domestic Cho Arc Cosponsor Nonoverlap Theorem) Domesfic(A) ACho arc(A) λ Cosponsor(B,C,A)

Not(Overlap(B,C)) .

294

8. CHO ARCS

Proof. Let B' and C' be cosponsors of domestic Cho arc A'. Suppose,

contrary to the theorem, that B' and C' overlap. Then it follows from the definition of "Successor" that A' is the successor of both B' and C'. Hence, The Cho Arc Second Sponsor Identity Law determines that B' overruns C' and that C' overruns B', a contradiction. QED. It is now possible to show that predecessors are unique: (42) THEOREM 65 (The Predecessor Uniqueness Theorem) Predecessor (Α, Β) Λ Predecessor (C, B) -» A = C . Proof. Suppose the contrary of the theorem. There are three cases to

consider: (i) multiple local predecessors, (ii) multiple foreign predeces­ sors, and (iii) some local and some foreign predecessors. Without loss of generality, consider the class of situations where B' has two distinct predecessors, A' and C'. It follows from Theorems 32, 33, 35, and 36 that A', B', and C' are all structural arcs. Case (i). If both A' and C' are local predecessors, then B' is domestic and has two D-Iocal sponsors. Hence, it follows from The Employed Domestic Arc Theorem that B' is a Cho arc. But this contradicts Theorem 64, which says that a domestic Cho arc cannot have distinct overlapping sponsors. Case (ii). Suppose A' and C' are both foreign predecessors. B' is then an immi­ grant arc. The Immigrant Local Sponsor Law requires that B"" have a local sponsor, necessarily distinct from A' and C', contradicting The Maximal Two Sponsor Law. Case (iii). Suppose, without loss of generali­ ty, that A' is a local, and C' a foreign, predecessor of B'. Again, as in case (i), B' is domestic and hence cannot be employed. But B' can­ not be a Cho arc either, since this would contradict Theorem 64. QED. Note that case (iii) might eventually be provable independently of The Employed Domestic Arc Theorem. (See the conjectured theorem (11.169).) This states that an arc parallel to an immigrant is necessarily an R-Local Successor of that immigrant. In case (iii) above, this would mean that A' is an R-Successor, as well as a predecessor, of B', which is impossible.

8.2. COSPONSORSHIP OF DOMESTIC CHO ARCS

295

Thus, the promissory note that predecessors were unique is paid, and the laws adopted yield a highly restrictive theory of both the successor and predecessor relations. Now that The Predecessor Uniqueness Theorem has been proved, we return to the delayed proof of Theorem 25, The Immigrant Intrusiveness Theorem, mentioned in Chapter 5, section 5. (43) THEOREM 25 (The Immigrant Intrusiveness Theorem) Immigrant(A) -> Intrusive(A) . Proof. Let A' be an immigrant arc and assume, contrary to the conse­

quent, that A' is domestic. It follows that there is a parallel sponsor of A', B'. There are two possibilities. Either B' is A' or not. But B' cannot be A' since A' has a distinct (from B') sponsor and distinct sponsors are precluded for self-sponsoring arcs by The Self-Sponsor Law. Therefore, AV B'. A' is then a successor of B', hence a local succes­ sor of B'. But, since A' is an immigrant by definition, it also has a foreign predecessor, necessarily distinct from B', contradicting The Predecessor Uniqueness Theorem. QED. With Theorem 25 proved, the disjointness of the sets of domestic arcs, immigrant arcs, and grafts, which collectively exhaust the set of arcs, has been formally guaranteed (see Theorem 28, The Graft/Organic Disjointness Theorem of Chapter 5, section 5). 8.3. The Chomeur Law In the previous sections, we sketched some major considerations bearing upon the treatment of Cho arcs, presented The Temporary Chomeur Condition, developed a set of PN laws controlling Cho arc distribution in well-formed PNs, proved several relevant theorems, and discussed certain side issues. The discussion centered on a "translation" into APG terms of the essential aspects of the RG view of the condition governing the occurrence of Cho arcs. We suggested that this formulation was too strong

296

8. CHO ARCS

in that it wrongly predicted the occurrence of Cho arcs in situations where we claim an overrunning arc itself erases the arc it overruns, as in (10a), (12b), and (16). In this section, some undesirable consequences of The Temporary Chomeur Condition are depicted, indicating that the "tradition­ al" view of chomeurs was faulty in a significant respect other than the one discussed in section 2. These considerations lead to a still further weakening of The Temporary Chomeur Condition, resulting in the state­ ment of the PN law which governs the distribution of Cho arcs within this version of APG, namely, The ChSmeur Law (but see section 7). With The Temporary Chomeur Condition in mind, consider the following artificial example: (44)

40

50

60

In this structure, E overruns D. IfTheTemporaryChomeurCondition were correct, no natural language clause could have the form in (44), be­ cause D is not the predecessor of a Cho arc, but of a 1 arc. The pretheoretical assumptions about the chomeur relation, which we have referred to on several occasions, in no way justify the view that (44) is necessarily ill-formed. For no violation of stratal uniqueness results in (44). Simply put, (44) is an illustration of a structure in which none of the pretheoretical motivations for Cho arcs require a Cho arc to appear. The implication is that The Temporary Chomeur Condition is a stronger principle than is justified by the motivations which originally led to its formulation. This is not necessarily a bad result, since one wishes in general to have the strongest set of claims compatible with known fact.

8.3. THE CHOMEUR LAW

297

In this case, however, we claim that The Temporary Chomeur Condition is too strong, wrongly excluding cases like (44) (see below for examples). (44) exemplifies the following set of circumstances: (45) (3A) (3B)(3C) (Overrun (Α, Β) Λ Local Successor (C, Β) Λ Employed (C) Λ Not ((3D) (Replace (D, B)))) . That is, (44) illustrates situations where one arc is overrun by another arc and has (i) a local successor which is riot a Cho arc and (ii) no replacer. 12 A in (45) corresponds to E in (44), B in (45) to D in (44), and C in (45) to C in (44). The reason that no case of the form (45) can lead to a violation of stratal uniqueness is identical to the reason that Cho arcs pre­ vent such violations. Since D, the overrun arc in (44), has no replacer, its local successor, C, locally assassinates D. TheFall-ThroughLaw prevents D from falling through into C's first stratum, c 2 , which is identical to the first stratum of the overrunner, E. Consequently, stratal uniqueness is preserved. If The Temporary Chomeur Condition were a PN law, it would be claimed, inter alia, that no examples of the form (44) could be found. We believe, to the contrary, that instantiations of (44) exist and this is one, but not the only, reason why we consider The Temporary Chomeur Condi­ tion excessively strong. To make the general problem more concrete, consider: (46) a. Ralph gave a book to Maxine. b. Ralph gave Maxine a book. c. A book was given to Maxine by Ralph. d. Maxine was given a book by Ralph. e. A book was given Maxine by Ralph.

an arc like D in (44) had a replacer, PN law 48, The Earliest Strata Uniqueness Law, would be contradicted. For both the replacer and E would be 2 arcs with first coordinate C 2 · Thus, there cannot be a well-formed PN with essentially the form of (44), except that, in addition, D has a replacer.

298

8. CHO ARCS

In accord with RG, we analyze the initial strata of (46a-e) as involving a 1 arc with P-head Ralph, a 2 arc with P-head a book, a 3 arc with P-head Maxine, and a P arc with P-head gave. (46e), which is of central interest here, involves, minimally, an additional stratum where a book is a P-head of a 1 arc, Maxine a P-head of a 2 arc, 13 Ralph a P-head of a Cho arc, and given a P-head of a P arc. This informal description, how­ ever, still allows the following two plausible (partial) analyses of (46e), one, (47a), incompatible with The Temporary Chomeur Condition, the other, (47b), consistent with it: (47) a.

Cho

a book

(was) given

Maxine

(by) Ralph

b.

Cho cIc

a book

(was) given

Maxine

2

(by) Ralph

13 The 3 arc whose head corresponds to Maxine in (47) is not associated with a prepositional flag. This is related to the fact that this 3 arc has a 2 arc local successor, precluding a flagging structure in our terms. See Chapter 13 for further discussion of flagging structures.

8.3. THE CHOMEUR LAW

299

The difference between (47a) and (47b) is that in the former B and E both have employed C2 local successors, while in the latter, only B has an employed C2 local successor, E having a c 3 local successor. (47a), having only two strata, is more "compact" than (47b), which has three strata. (47a) is incompatible with The Temporary ChSmeur Condition since D overruns B, but B does not have a Cho arc successor. Rather B has a 1 arc successor, A . Thus, (47a) is a model of (44). Although (47a) is more elegant than (47b) and deserves serious con­ sideration because it does not have "excrescent" strata, i.e., has the same set of incomplete arcs as (47b) but only two strata, there is no evi­ dence known to us which unequivocally rules out (47b). Moreover, since the adoption of (47a) would entail weakening The Temporary Chomeur Condition, partially offsetting the advantage of (47a), it is hardly clear which option to choose. There are other data, however, discussed below, which we take to indicate that structures of the form (44) do exist. Before dealing with some of this, we provide a more compact notation for repre­ senting the relevant aspects of PNs such as (47a,b) and then further illustrate the general problem. With regard to the structure of the initial and final strata of (46e) as described above, the relevant information can be conveniently represented as follows: (48) C1 cn

Ralph

a book

Maxine

1

2

3

Cho

1

2

(48) is interpreted as follows: the labels for the columns, Ralph, a book, and Maxine are understood as representing P-heads of arcs with the same tail node, which, we know from Chapter 7, section 5, must be a basic clause node. By providing an R-Sign and a coordinate, the rows specify successive arcs of which the column labels represent P-heads. Thus, e.g., Ralph is a 1 at C1 and Maxine is a 3 at C1 . Maxine is also a 2

300

8. CHO ARCS

at c n . Repetitionofan R-Sign, R, over rows Cj,---,c- indicates that the column label represents the P-head of an arc with R-Sign R and coordinate sequence (this aspect of the convention is illus­ trated below). With this interpretation, it should be evident that (48) represents the relevant aspects of the R-graph structure of (46e) common to (47a,b). The question of current theoretical interest is, broadly, whether any strata intervene between the

C1

stratum and the

Cfl

stratum in, e.g.,

(48), i.e., whether or not C n =C 3 . Further, if c fl is not C 2 in (48), what is the number and character of the intervening strata? To facilitate discussion of situations like (48), we introduce the following definition: (49) Def. 139: Let A, B and C be three distinct, neighboring arcs. Then: Potentially Term Incompatible (A, B) Term arc (A) C j^ A

λ

Β)

λ

Term x arc (Β λ C)

λ

λ

R-Successor (A, C) .

That is, two distinct neighboring arcs, A and B , are potentially term incompatible if and only if (i) A is a Term arc, (ii) A and B are both Cj i arcs, (iii) B and C are both Term x arcs, and (iv) A is the R-Successor of C . Referring to (47a,b), in both, A is potentially term incompatible with D. This is so since, in both cases, A is a c n Term arc, D is a

Cn

2

arc, and A is an R-Successor of 2 arc, B. The basic idea behind situations involving potential term incompatibili­ ty is that, depending upon particular assumptions, conditions for the intro­ duction of Cho arcs could arise. A priori any of the following representa­ tions might be correct for (46e): (50) cI C2

Ralph

a book

Maxine

1

2

3

Cho

1

2

301

8.3. THE CHOMEUR LAW

Ralph C1 C2 C3

(52)

a book

Maxine

1

2

3

Cho

1

3

Cho

1

2

Ralph

a book

Maxine

1

2

3

1

Cho

2

Cho

1

2

C1 C2 C3

(47b)

Analyses like (50) will be referred to as compact representations. The defining characteristic of a compact representation is, roughly, that there is more than one "relational change" between two successive strata in­ volving only employed arcs. More precisely, an analysis is compact if it involves a stratum with more than one motivated, employed arc. For instance, in (50), there are two motivated, employed c 2 arcs, the 1 arc and the 2 arc. On the other hand, in (51), the c 2 nd stratum has only one motivated, employed arc, the 1 arc. Similarly, the C 2 nd stratum of (52) has only one motivated, employed arc, the 2 arc. Hence, of the three, only (50) is compact. In (50), the C 1 2 arc and the C 1 3 arc are both predecessors of employed c 2 arcs. In contrast, in (51) and (52), "simultaneous employed arc spon­ soring" does not occur. In (51), the only relevant difference between the C 1 and c 2 strata is the appearance of the 1 arc successor of the C 1 2 arc. Sponsoring of the 2 arc by the overlapping C j 3 arc is "delayed" in (51). Thus, (51) involves one more stratum than (50), but does not in­ volve any extra, distinct incomplete arcs. In (52), on the other hand, sponsoring of the 2 arc by the overlapping C 1 3 arc takes precedence over any other sponsoring, and, hence, the environment for the introduction

302

8. CHO ARCS

of an "extra" Cho arc is created. Because there is a C 2 2 arc in (52) which overruns a C 1 2 arc, the latter, since it is not erased by its overrunner (and indeed cannot be, in this case), must, by The Temporary Chomeur Condition, necessarily sponsor a C 2 Cho arc successor. As observed earlier, The Temporary Chomeur Condition precludes the compact analysis, (50), for (46e). This condition implicitly claims (50) is the wrong representation for (46e). On the other hand, it makes no claims con­ cerning the relative merits of (51) and (52). The key difference between the latter two analyses is whether the predecessor of the C 3 1 arc is a Cho arc or a 2 arc. Before continuing the theoretical discussion, we present other exam­ ples involving potential term incompatibility: 14 (53) a. John seems to me to sing. b. (i)

me C2 c3

John

to sing

1

2

Cho

3

1

Cho

(ii) C2 C3

C4

C2 C3

C4

me

John

to sing

1

2

Cho

Cho

1

Cho

3

1

Cho

me

John

to sing

1

2

Cho

3

2

Cho

3

1

Cho

The main clause of (53a) involves, we claim, a C 2 stratum with me as 1, John as 2, and to sing as chomeur, and a later stratum with me as 3, John as 1, and to sing as chomeur. 15 That is, (53a) involves inversion.

1 ^The Sinhalese examples in (55) are from Berman (1975), the Dyirbal exam­ ples in (56) from Dixon (1972). We have revised the transcription of the Sinlialese examples in accord with information given to D. Perlmutter by J. Gair, from whose work Berman obtained the examples. 15 (53a) involves raising. TTie CjSt stratum of the main clause involves me as 1 and a clause corresponding to John sings as 2 .

303

8.3. THE CHOMEUR LAW

(53b, i, ii, iii) are the various analyses of (53a) consistent with this gen­ eral inversion analysis of (53a). (53b, i) is compact, (53b, ii, iii) noncompact. (54) a. That is known to the FBI. b. (i)

(ii)

FBI that C1

°2

1

2

C1

3

1

C2

(iii)

FBI

that

1

2

C1

3

2

C2

3

1

c3

C3

FBI that

1

2

Cho

1

3

1

(54a) is analyzed as having a C1 stratum with FBI as 1 and that as 2, and a later stratum with FBI as 3 and that as 1. Thus (54a), like (53a) is claimed to involve inversion. Of the possible analyses of (54a), (54b, i) is compact and (54b, ii, iii) are noncompact. (55) Sinhalese16 a. mams I b. mama I c. maTa

pol

kaDanawa

coconuts pick atin

pol

= "I am picking coconuts." kaeDenawa

by hand of coconuts pick-passive = "I can pick coconuts." pol

kaeDenawa

I-Dative coconuts pick-passive = "I have to pick coconuts." d. Possible Partial Representations of (55c)

16 Sinhalese passives like (55b) differ in meaning from actives like (55a) in that the former express the initial subjects' ability to do something. Sentences like (55c) also differ in meaning from actives in that they convey the information that the initial subject must do something. We view these meaning differences as indicating that (i) sentences like (55b,c) involve L-graph arcs not present in S-graphs, which represent these semantic differences and (ii) passivization, rele­ vant to (55b) (see below), and inversion, relevant to (55c) (see below), are "trig­ gered" by these L-graph structures. We see no reason to regard these meaning differences as showing that (55a,b,c) are not syntactically related as described in the text.

304

8. CHO ARCS

(55a) is an active clause syntactically related to (55b), a normal passive. (55c) involves, we suggest, both passivization and inversion. Our basic claims regarding (55c) are that it involves an initial stratum with maTa as 1 and pol as 2, and a later stratum with maTa a 3 and pol a 1. (55d, i) provides the compact analysis of (55c), (55d, i, ii) noncompact ones. (56) Dyirbal a. Balan nc

dyugumbil bajjgul

yayangu

bajjgu

woman-Abs nc

man-Erg

nc

yugungu

balgan

stick-instrument

hit = "The man hit the woman with the

stick." b. Bala yugu nc

stick-Abs

barjgul yayangu bagal-ma-n nc

man-Erg hit-affix-tense

bagun dyugumbilgu nc

woman-Dative = "The man hit the woman with the stick."

c. Possible Partial Representations of (56b)

8.3. THE CHOMEUR LAW

305

(56a) is an active, transitive single stratum sentence with barigul yaya-qgu as initial and final ergative, balan dyugumbil as initial and final absolutive 2, and bar/gu yuguj]gu as initial and final instrument. (56b) is a variant in which bagun dyugumbilgu is, we assume, a final 3 and bala yugu a final absolutive 2. We analyze (56b) as involving an initial stratum ex­ actly like the initial stratum of (56a). (56c, i) is the compact analysis of (56b), (56c, ii, iii) the noncompact analyses. The Temporary Chomeur Condition also prohibits analyses (53b, i), (54b, i), (55d, i), and (56c, i). For example, in (56c, i) the 2 arc in stratum c 2 overruns the 2 arc in stratum C 1 and, hence, must, by The Temporary Chomeur Condition, either erase the C 1 2 arc, impossible in this case, or else a c 2 Cho arc must be the successor of the C 1 2 arc, which is inconsistent with (56c, i). More generally, in each of the above cases, the compact analysis is precluded by The Temporary Chomeur Condition by· virtue of the fact that the earliest stratum and the subsequent stratum in­ volve Overrun. In all such cases, The Temporary Chomeur Condition would force a "delay" in order to prevent the occurrence of "intermediate" Cho arcs. Since we believe the blocking of compact PNs to be an error in cer­ tain cases (e.g., in (54a) and (55c)), we propose in (57) below a weaker principle in place of The Temporary Chomeur Condition, The Chomeur Law. This PN law permits compact representations in a variety of situations such as (50), (53b, i), (54b, i), (55d, i), and (56c, i). The Chomeur Law con­ stitutes, in effect, a further weakening of the RG view of the principle governing the occurrence of chomeurs. (57) PN Law 62 (The Chomeur Law) (3A) (Ck -Overrun (A, B) A Not ((3c) (c k (C) Λ Employed (C) Λ Local Assassinate(C, B))) «-+ (3D) (Cho arc (D) Λ < C K /3 > (D) Λ Successor (D, B)) . PN law 62 states that a Cho arc is the successor of a given Term arc just in case that Term arc is overrun and is not locally assassinated by an em­ ployed arc. The coordinate specification, c k , guarantees that the over-

306

8. CHO ARCS

runner and the Cho arc appear for the first time in the same stratum, pre­ serving stratal uniqueness. The significant difference between PN law 62 and The Temporary Chomeur Condition is that, in the latter, the only admissible employed local eraser of an overrun arc is the overrunner. Within the constraints imposed by independent PN laws, PN law 62 permits any local assassin to obviate the necessity for the occurrence of a Cho arc. For example, re­ turning to (50), the c 2 1 arc is a local assassin of the C 1 2 arc, which is overrun by the C2- 2 arc. Unlike The Temporary Chomeur Condition, The Chomeur Law does not require the presence of "extra" Cho arcs or "extra" strata in the PNs of sentences such as (46e). Similarly, (53b, i), (54b, i), (55d, i), and (56c, i) are all compatible with The Chomeur Law. But nothing so far stated entails that these compact analyses are the cor­ rect ones. The Chomeur Law does not block noncompact analyses like (51), (52), (53b, ii) and (53b, iii), (54b, ii) and (54b, iii), (55d, ii) and (55d, iii), and (56c, ii) and (56c, iii). Our view is that compact representations are correct in some, although not in all, cases. For example, we claim that (50), (54b, i), (55d, i), and (56c, i) are correct. On the other hand, we believe that the noncompact analysis (53b, ii) is correct for (53a). Hence, we introduced The Chomeur Law, which is weaker than The Temporary Chomeur Condition in that it allows compact analyses, although it does not block noncompact ones. To illustrate the motivation for permitting both compact and noncompact analyses, consider (53a) and (55c). Within the current framework, as in RG, there is, in both cases, an early stratum having both a 1 and a 2. Similar­ ly, in both cases, there is a later stratum where the head of the earlier 1 arc is the head of a 3 arc, and the head of the earlier 2 arc is the head of a 1 arc. However, there is a relevant difference between the two cases: (55d), but not (53a), exhibits passive morphology. Informally, we account

for this contrast as follows. We claim that the grammar of English does not allow representations such as (53b, i) for clauses with verbs like seem. In clauses with verbs like ieem, an accusative arc cannot have a 1 arc

307

8.3. THE CH6MEUR LAW

local successor (in more traditional terminology, passive is blocked in such cases). Hence, the compact analysis, (53b, i), is out for (53a); (53b, ii) being, we claim, the correct treatment. Thus, the correct PN for (53a) is in relevant respects like the one given for the Georgian inversion example, (7.88b,c), repeated below. (7.88) b.

turme

deidas

apparently aunt-Dat

umyeria she-sang-it-III-3

nanina Iullaby-Nom =

"Apparently Aunt has sung a lullaby." c.

deidas

naniria

In English, Georgian, and many other languages, there are clauses which involve, inter alia, a stratum, Cj c , with an ergative arc and an accusative arc, a successive stratum with a 3 arc successor of the ergative arc; the Cji accusative arc being unaccusative at c^ +1 , and a ο^ +2 stratum, with a 1 arc successor of the C^ 1 unaccusative arc, this last "transi­ tion" forced by The Unaccusative Law, described in Chapter 7. Sinhalese, in contrast to English and Georgian, countenances struc­ tures like (55d, i) for clauses with verbs like kaeDenawa "pick." That is, Sinhalese grammar countenances "simultaneous" succession of an erga­ tive arc by a 3 arc and an accusative arc by a 1 arc. Using the concepts of contrastive 3 arc and simple 3 arc mentioned in Chapter 7, note 30, these facts can be stated by postulating that Sinhalese permits an ergative arc to be the local predecessor of a simple 3 arc. This, coupled with passivization, yields the desired results, predicting occurrence of passive morphology. Compare (55c) to (55a,b). (55a) is an active sentence and

308

8. CHO ARCS

lacks passive morphology. (55b) is a passive clause and has passive mor­ phology, just as (55c). The difference between (55b,c) is the occurrence of the flag material atiri "by hand of" in (55b), indicating, we assume, that a Cho arc is the local successor of the early 1 arc, rather than Dative case, indicative of a 3 arc in (55c). We thus take the correct analysis of (55b) to be: (58) cI C2

mama (a tin)

pot

1

2

Cho

1

Both (58) and (55d, i), involve the succession of an accusative arc by a 1 arc. Further, both involve a C 2 1 arc which overruns a C 1 1 arc. But only in the latter is the overrun arc the local predecessor of a Cho arc. The formal parallels between (55d, i) and (58) embody, in APG terms, the basic RG insights regarding passivization (see Perlmutter and Postal [1977] and Postal [1977]). In APG terms, passivization is formally char­ acterized as the local succession of a

accusative arc by a c^+1 1

arc, illustrated by the second columns of (55d, i) and (58). Passive mor­ phology, then, is dependent upon this formal feature. Local succession of an accusative arc by a 1 arc is a necessary condition for "triggering" passive verbal morphology. 17 Diagrammatically: (59) ck c k+l

accusative 1

Necessary formal condition for passive verbal morphology.

17 That this is not a sufficient condition is shown, inter alia, by so-called re­ flexive passives. In APG terms, these involve replacers of accusative arcs as well as 1 arc local successors for these, as in (IOb) in section 2 above. In (10b), B is a 1 arc local successor of the accusative arc, C, which is replaced by D, P-headed by the reflexive pronoun sich. There seems to be at least a strong ten­ dency for reflexive passive constructions not to manifest any special passive verbal morphology. See Chapter 11, section 8.

8.3. THE CHOMEUR LAW

309

This contrasts with the local succession of an unaccusative arc by a 1 arc, as in example (53b, ii), which does not "trigger" passive verbal morphology. In contrast to (55d, i) and (58), (53b, ii) does not meet the condition in (59). While we cannot present here a detailed justification of the APG account of this area of grammar, it should be clear how (53b,ii), and (55d, i) provide, in conjunction with (58), the basis for a formal account of the presence or absence of passive verbal morphology. Now let us reconsider (54). (54) has passive verbal morphology, which we claim is "triggered" in part by the fact that the grammatical rules of English countenance (54b, i) but not (54b, ii) for clauses with the verb know . 18 Hence, the rule which countenances passive verbal morphology

is applicable in cases such as (54a). Although we are skirting important issues, the general motivation behind noncompact analyses in certain cases should be clear. A major difference between the APG conception of the role of Cho arcs and the past RG view is that, within APG, compact PNs involving poten­ tial term incompatibility are allowed. This circumvents the necessity of allowing Cho arcs to sponsor Term arc successors. This is in direct con­ trast to the RG view of chomage, represented in APG terms as (5) above. For example, return again to (54a). To account for the passive verbal mor­ phology in a straightforward manner, we assume with RG that (54b, ii) is an incorrect representation of (54a), sjnce it fails to meet (59). Since RG involved a view of chomeurs which precluded an analogue to the compact analysis, (54b, i), within that framework, only an analogue to (54b, iii) was possible for (54a). (54a) would then within RG have been assumed to in­ volve, inter alia, three consecutive strata, Cji, Cj tfl , and Cj tf2 , such that: (i) stratum Cjc included a 1 arc with P-head the FBI and a 2 arc I O

Even if known in (54) turns out to be properly analyzed as not involving passivization, i.e., if it is really an adjective like obvious, clear, etc., the gen­ eral point that passivization and inversion can "occur simultaneously" is still supported by, e.g., the evidence from Sinhalese discussed above.

310

8. CHO ARCS

with P-head that ; (ii) stratum Cjcfl included a 1 arc with that as P-head and a Cho arc with the FBI as P-head; and (iii) stratum Cj if2 included a 3 arc with the FBI as P-head and a 2 arc with that as P-head, In other words, the RG view of a sentence like (54a) necessitated the "advance­ ment" of a chomeur to 3. In present terms, this would amount to having a Cho arc sponsoring a 3 arc. Similar comments hold for (55c) and (56b). Of the analyses (55d, i, ii, iii) and (56c, i,ii, iii), only (55d, iii) and (56c, iii) are descriptively adequate and consistent with the RG view of chomage. But these structures involve (language-particular) local succession of Cho arcs by Term arcs. There is no evidence known to us favoring, e.g., the intermediate C2 stratum in (54b, iii), necessitated by (5) and The Temporary Chomeur Con­ dition. It thus seems possible to tighten the current theory by imposing the constraint that a Cho arc cannot have a local successor: (60) PN Law 63 (The Cho Arc No Local Successor Law) Cho arc (A) -> Not ((3B) (Local Successor (B, A))) . While The Chomeur Law is, from one perspective, weaker than (5) and The Temporary Chomeur Condition, it is stronger than both in the follow­ ing ways. It (i) permits compact representations for PNs , eliminating "excrescent" strata in a multitude of cases, and (ii) permits the imposi­ tion of PN law 63, which prevents Cho arcs from having local successors, thus tightening the theory in other areas. Hence, we tentatively conclude PN law 62 is the correct principle governing chomage (but see section 7). 8.4. The Stratal Compactness Law The preceding section touched on the topic of compact PNs in cases involving potential term incompatibility. The general issue of compact­ ness arises in cases not involving potential term incompatibility, and even in situations independent of Cho arc considerations. Such situations are illustrated by the following hypothetical examples:

8.4. STRATAL COMPACTNESS LAW

311

In (61)-(63), the first and last row of each variant within each example is the same. Comparing across variants within each example, looking down an aibitary column, each label, a, b, or c, has the same "basic history." For example, consider (61a,b,c). The head of the arcs represented in the first column, the a column, is, in each case, a 1 and then subsequently a chomeur. Looking at the third columns in (61), in each case, the head represented by c is a Ben and subsequently a 3. The variants within a given example are only "trivially" distinct. These

312

8. CHO ARCS

variants, while differing in the number and character of strata, involve the same set of incomplete arcs. (64) below provides a real example from French of a compact PN: (64) a. Le bras

Iui

a

ete casse par Pierre.

"The arm to him has been broken by Pierre" = "His (somebody else's) arm was broken by Pierre."

(par) Pierre (le)bras

Iui

In terms of the notation introduced in this chapter, the clause whose point is 8 would have the structure shown in (65): (65) a.

6 cI

2

C2

1

Iui

Pierre 1

3

Cho

b.

6 cI C2 C3

Iui

Pierre 1

2 2

3

1

1

3

Cho

(65a) involves only two strata, the same number required to account for a passive clause without an immigrant 3 arc. This contrasts with the noncompact structure, (65b), which has three strata. The important aspect of (65a) is that it does not involve potential term incompatibility. We would like to impose a PN law which "forces" PNS to be compact in cases where there is no potential term incompatibility. To do this, we first introduce two defined constructs: Compactness Candidate and Earliest Compactness Candidate: Supposethat X = D-Sponsor (A, B) and

8.4. STRATAL COMPACTNESS LAW

313

Y = D-Sponsor (C, D), Tail (A) = Tail (B) = Tail (C) = Tail (D) = b , and D does not sponsor A . Then X is said to be a compactness candidate with respect to Y if and only if (i) A has more than one coordinate, i.e., has fallen through, and (ii) there is no pair Z = D-Sponsor (U, R) such that Tail (U) = Tail (R) = b and one of the arcs in Z has the same Term R-sign as either A or B . (i) is necessary to maintain consistency with the coordinate determination laws, as discussed further below, (ii) is designed so as not to " f o r c e " a PN to be compact in cases involving potential term incompatibility. Suppose that X = D-Sponsor (A, B) and X is a compactness candidate with respect to Y . Then X is said to be an earliest compactness candidate with respect to Y if and only if there is no other sponsor pair, Z = Sponsor (C,D) , such that X is a compactness candidate with respect to Z and D's first coordinate index is less than B ' s . This construct will be used to insure that PNs are as compact as possible. Formally: (66) a. Def. 140: Let X = D-Sponsor (A, B) and Y = D-Sponsor (C, D) such that Not (Sponsor (D, A)) and A , B , C , and D are four distinct arcs with tail b. Then: and

Compactness Candidate (X, Y) (ii) Not

D-Sponsor(U,R)

b. Def. 141: Suppose Y = Sponsor (A, B) A (B). Earliest Compactness Candidate (X,Y) Candidate

Then:

«-» Compactness Compactness

Candidate (X, Sponsor We can now state The Stratal Compactness Law, which has the effect of blocking noncompact PNs in cases not involving potential term incompatibility:

314

8. CHO ARCS

(67) PN Law 64 (The Stratal Compactness Law) Earliest Compactness Candidate (Sponsor (A, B), Sponsor (C, D)) Λ < Cj β > (B) A(D) -> j = k . The Stratal Compactness Law says the following. Suppose there are two sponsor pairs, X=Sponsor(A 1 B) and Y = Sponsor(C,D) such that X is an earliest compactness candidate with respect to Y . Then B's first coordinate index is identical to D's. So, under the condition of earliest compactness candidate, PN law 64 insures that there will not be any "excrescent" strata. A few comments are in order about the formulation of the definition of "Compactness Candidate." D-Sponsor was used, rather than Sponsor, to prevent The Stratal Compactness Law from applying in cases like: (68) a. Ben\ci

α

b

c

b.

In (68a), if Sponsor(C,B) were a compactness candidate, and hence an earliest compactness candidate, with respect to Sponsor (A, A), then The Stratal Compactness Law would "require" the first coordinate of B to be C1 , violating The Local Successor Coordinate Law. Hence, there would be no well-formed PN with (68a) as a subpart.

315

8.4. STRATAL COMPACTNESS LAW

(i) of (66a) is needed to prevent The Stratal Compactness Law from applying erroneously in cases where a given PN cannot be more compact. For example, if Sponsor (B,C) in (68b) were an earliest compactness candidate with respect to Sponsor(E, D), The Stratal Compactness Law would "force" the first coordinate of C to be C 2 . This would be incon­ sistent with both The Local Successor Coordinate Law and The Ghost Coordinate Law (B is a ghost arc in (68b)). However, since B has only one coordinate, the pair Sponsor (B,C) fails (i) of the definition of "Com­ pactness Candidate" and is thus "exempt" from The Stratal Compactness Law. The Stratal Compactness Law, can be illustrated by the following hypothetical PN fragment: (69)

c K"

Ber

α

b

Since (69) contains three motivated strata, either C or D must have two coordinates. Suppose (C) and (D). Then, Sponsor(C, D) would be a compactness candidate with respect to both Sponsor (Β, E) and Sponsor(A f B). However, Sponsor(C 1 D) would be an earliest com­ pactness candidate only with respect to Sponsor (A, B) . Tlje Stratal Com­ pactness Law would then block (69), since Cjf = C3 and not c 2 as required. Hence, for (69) to satisfy The Stratal Compactness Law,

316

8. CHO ARCS

(C) and (D) would have to hold, as desired. That is, (70a) but not (70b) is precluded by The Stratal Compactness Law.

c

C

C

I

a Ben

b Loc

2

3

3

2

b. C1

a Ben

b Loc

Loc

c2

3

1

1

C3

2

1

Thus, in this ease, The Stratal Compactness Law does not have the effect of reducing the number of strata. But it still forces "things to happen as early as possible," and, hence, even in such situations makes predictions concerning the character of the strata. Without a principle such as The Stratal Compactness Law, many, only trivially distinct, alternate analyses of many sentences would be possible. PN law 64 is then a major step toward blocking excrescent analyses. We have eliminated noncompact PNs in "noninteracting" situations and have allowed for both compact and noncompact representations in situa­ tions involving potential term incompatibility. The proper analyses in the latter cases must then be picked out by currently unknown laws or by language-particular rules.

8.5. The Strata! Uniqueness Theorem In Chapter 7, we presented The Earliest Strata Uniqueness Law, re­ peated in (71) below, and claimed that from this and other, independently needed PN laws, one could prove the more general Stratal Uniqueness Theorem, repeated in (74) below. (71) PN Law 48 (The Earliest Strata Uniqueness Law) Term x arc ( A A B )ANeighbor ( A 1 B) Λ

< C J C O > ( A ) A < ΰ ^ / 8 >(Β)

A =

B

.

To facilitate the proof of The Stratal Uniqueness Theorem, we first prove that (i) Cho arcs invariably assassinate their predecessors, and (ii) two neighboring Cj c Term x arcs are necessarily overrun linked.

317

8.S. STRATAL UNIQUENESS THEOREM

(72) THEOREM 66 (The Cho Arc Predecessor Local Assassination Theorem)

Cho arc (A) A Successor (A, B)

->

Local Assassinate (A, B) .

Proof. Suppose A' is a Cho arc successor of B'. A' must be domestic, since it cannot be an immigrant by The No Immigrant Cho Arc Theorem or a graft, since grafts cannot, by definition, have predecessors. Hence, it follows from The Successor Uniqueness Theorem and The Organic Cho Arc Local Successor Theorem that A' is the local successor of B'. Further, The Chomeur Law determines that B' is a Term arc and, hence, outranks the nonTerm arc A'. Therefore, it follows from PN law SO, The Demotion No Replacer Law, that there is no arc which replaces B'. Via The Successor Erase Law, A' then erases B' and, given Successor irreflexivity, locally assassinates B'. QED.

(73) THEOREM 67 (The Term Arc Overrun Theorem) Terrn x arc(AAB)A Neighbor(A,B)Ack(AAB)AAiB

->

Linked-Overrun(A,B).

Proof. Suppose A' and B' are two distinct neighboring Term x arcs. Clearly, if A' and B' share a coordinate, there must be some earliest coordinate that they have in common, say c m . Further, c m must be the first coordinate of ei ther A' or B'. If not, then A' and B' would both be c m_ 1 arcs, contradicting the assumption that c m is the earliest shared coordinate. It also follows that c m cannot be the first coordinate of both A' and B'. Otherwise, The Earliest Strata Uniqueness Law would be violated, since A',fo B' by hypothesis. Without loss of generality, consider just the case where the first coordinate of A' is c m ' Then: (i) A'=[Termib,a)] and B'= [Termib,c)] . Thus, by the definition of "Overrun", Overrun (A', B'). Hence LinkedOverrun(A',B'). QED. (74) THEOREM SS (The Stratal Uniqueness Theorem)

Term x arc (A AB) A Neighbor (A, B) ACk(A AB)

->

A=B .

318

8. CHO ARCS

Proof. Suppose that A' and B' are two neighboring Cjf Termx arcs but

that AV B'. Then, by Theorem 67, it follows that Linked-Overrun(A', B'). Without loss of generality, suppose that A' overruns B'. Let c m be the first coordinate of A'. That is: (i)

Cm -Overrun (A', B') λ c^A'aB') .

Next, we want to show that there is a c m arc which locally assassinates B'. Suppose there is no such arc. Then, in particular, no employed c m arc locally assassinates B': (ii)

Not ((3G) (cm(G) a Employed (G) a Local Assassinate (G, B'))) ·

But, by The Chomeur Law, there is then some arc, C', such that: (iii) Cho arc (C) a Cm (C) λ Successor (C, B') . Hence, Theorem 66, The Cho Arc Predecessor Local Assassination Theorem, and (iii) determine that: (iv) Local Assassinate (C, B') a Cffl (C) . But (iv) contradicts the assumption that no such arc exists. Hence: (v)

(3D) (cm(D) a Local Assassinate (D, B')) ·

By The Fall-Through Law, (v) entails that B' cannot be a c m arc. Hence Cn^1

is the last coordinate of B'. But, since Cffl-Overrun (A', B') , Cffl

is the first coordinate of A'. Therefore: (vi) Not ((3r) (c r (A'ABO)). But (vi) contradicts (i). QED. Thus, it is provable from APG assumptions that any given stratum can have at most one Termx arc, i.e., at most one 1 arc, one 2 arc, and one 3 arc. This theorem, which embodies the essence of the earlier Stratal Uniqueness Law (see Perlmutter and Postal [1977]), shows that APG is not consistent with views expressed in, e.g., Berman(1975), Keenan(1975), and Gary and Keenan (1977), to the effect that, in present terms, a given stratum can contain more than one Termx arc. At this point, we can discuss the interaction of The Chomeur Law and The Overrun Erase Theorem, proven in (76) below with the aid of The Stratal Uniqueness Theorem. The Overrun Erase Theorem states that if A overruns B and B does not have a local successor, then A erases B.

8.5. STRATAL UNIQUENESS THEOREM

319

The proof of The Overrun Erase Theorem depends on The Zeroing Out­ flank Law, whose rationale is discussed further in Chapter 9. (75) PN Law 65 (The Zeroing Outflank Law) Local Zeroes (A, B) ANominal arc (B) -» Outflank(A 1 B) . PN law 65 insures that local zeroing of a Nominal arc involves outflanking. (76) THEOREM 68 (The Overrun Erase Theorem) Overrun (A, B) AiVoi ((3C)(Loca/ Successor (C, B))) -> Erase(A,B) . Proof. Suppose contrary to the theorem that there are arcs A' and B'

such that Overrun (A', B') and Not ((3C) (Local Successor (C, B'))) , but such that: (i)

Not (Erase (A', B')).

Further, suppose: (ii)

CJ f -Overrun (A', B').

Since B' has no local successor by hypothesis and hence, in particular, no Cho arc local successor, some employed arc, say D'= A', with coordi­ nate Cj c , must locally assassinate B'. Otherwise, the antecedent of The Chomeur Law would hold, yielding a contradiction of the assumption that B' has no local successor. Therefore: (iii) Local Assassinate (D', B') A D'= A' A CJ { (D'). Next, we show that D' and B' do not overlap. Suppose they do. Then, B' and D' would be parallel and so, by PN law 11, The Parallel Assas­ sin Law and (iii), it follows that D' is the local successor of B', con­ tradicting the original assumption that no such local successor exists. Hence: (iv) Not (Overlap (D', B')). Moreover, since B' is a Term arc, hence a Nominal arc, this, in conjunc­ tion with (iii) and (iv) entails that: (v)

Zeroes (D', B') A Nominal arc (B').

Thus, via PN law 65, The Zeroing Outflank Law: (vi) Outflank (D', B').

320

8. CHO ARCS

Hence, from (vi), the fact that B' is a Term arc, and the assumption that D' is a Cj c arc, it follows that: (vii)

Cj i -Overrun (D',

B').

But (vii) and (ii) contradict The Stratal Uniqueness Theorem, since A' ^ D' by hypothesis. QED. The upshot of The Overrun Erase Theorem is that, given Overrun, there are two possibilities, as illustrated in (77a,b,c) below. Either the overrun arc is erased by the arc which overruns it, like Erase (A, B) in (77c), or the overrun arc has a local successor, either employed, like A in (77a), or a Cho arc, like A in (77b), which necessarily erases it. This lawfully determined division of cases, given Overrun, is of considerable importance in formalizing rules to determine PN well-formedness (see Chapter 14). For, as a result of PN law 62, The Chomeur Law, and The Overrun Erase Theorem, sponsor pairs linking Cho arcs to their predeces­ sors, as in (77a,b) below, and erase pairs linking overrunning arcs to the arcs they overrun, as in (77c) below are universally determined. (77) a.

AWWWWWW

V*vw\

Rolph

α book

Maxine

(was) given

8.5. STRATAL UNIQUENESS THEOREM

321

'/ c I c 2

Melvin

children

algebra

teaches

C.

Melvin children

UN

teaches

In (77b), since B is overrun by D , the successor of C , and yet is not locally assassinated by an employed arc, The Chomeur Law requires a Cho arc successor for B. On the other hand, in (77c), the overrun arc, B, does not have a local successor. Thus, The Overrun Erase Theorem re­ quires that the overrunning arc, A, erase B, as it does.

8. CHO ARCS

322

Put differently, The Overrun Erase Theorem suffices to preserve stratal uniqueness in all cases of Overrun because it permits, under such conditions, only the possibilities discussed above. Both of these insure, via The Fall-Through Law, that the overrun arc cannot fall through into the first stratum of the overrunning arc. This is shown by the following: (78) THEOREM 69 (The Overrun Arc Assassination Theorem) Overrun (A, B) -» (3C)(Locai Assassinate (C, B)) . Proof. Suppose that A' overruns B'. Then, via The Overrun Erase Theorem, either A' erases B', and hence B' is assassinated, or else there is some arc, C', which is the local successor of B'. Suppose the latter. Then, either there is some replacer of B', which would, by The Replacer Erase Law, erase, and hence assassinate, B', or, by The Suc­ cessor Erase Law, the local successor itself erases, and hence assassi­ nates, B'. QED. The Cho Arc Predecessor Local Assassination Theorem also deter­ mines that successors of arcs with replacers are always employed: (79) THEOREM 70 (The Replacee Employed Successor Theorem) Replace(Α, Β) Λ Successor (C, B) -> Employed(C) . Proof. Suppose that A" replaces B', C' is the successor of B' and, contrary to the theorem, that Cho arc (C'). Then, via The Replacer Erase Law, Erase (A', B') , and, via Theorem 66, The Cho Arc Predecessor LocalAssassinationTheorem, Erase (C', B'). ButthisviolatesThe Unique Eraser Law, since A'^ C', as the class of replacers and the class of successors are disjoint. QED. More informally, Theorem 70 shows that, within the current theory, demo­ tion of a term to a chomeur never "leaves a copy." This contrasts with the situation with heads of employed predecessors, which can in principle "leave copies." For example, in (10b), repeated below, the employed suc­ cessor of C, B, co-occurs with a replacer of C, D. Informally, sich, the

8.5. STRATAL UNIQUENESS TOEOREM

323

head of D, is a "copy pronoun" (see the discussion of pronominal arcs and copy pronouns in Chapter 11). (10) b.

sagen (nicht)

solche Sachen sich

8.6. Clause unions and The Chomeur Law

Chapter 7 briefly introduced the APG account of clause union construc­ tions. In this section, we look more closely at clause unions and, in particular, discuss how our explication of such constructions avoids un­ desirable interaction with The Chomeur Law. Clause union constructions generally involve situations where there is an immigrant 2 arc which is a neighbor of a self-sponsoring 2 arc. Such a situation could conceivably involve Overrun and hence perhaps cause the "introduction" of Cho arcs. The present treatment of clause union constructions, however, prevents this. We also take this opportunity to develop PN laws which govern clause union constructions. The type of construction we are concerned with is exemplified in (80):19 (80) a. French i.

Pierre a

fait partir Marie.

(= 7.65)

Pierre has made leave Marie = "Pierre had Marie leave."

19 Hiere is now an extensive literature on the subject. See, inter alia, Aissen (1974a, 1974b), Aissen and Perlmutter (1976), Cole and Sridhar (1976), Comrie (1974b, 1976), Frantz (1976), and references cited therein.

324

8. CHO ARCS

ii. J'ai

fait chanter la chanson a Pierre.

I had made

sing

the

song

to Pierre = "I had Pierre

sing the song." b. Turkish i.

Hasan ben-i

aga-t-ti.

Hasan me-acc cry-caus-past = "Hasan made me cry." ii. Hasan

kasab-a

et-i

kes-tir-di.

Hasan butcher-dat meat-acc cut-caus-past = "Hasan had the butcher cut the meat." c. Japanese i.

John ga Mary ο

ik-(s)ase-ru.

John nom Mary acc go-cause-tense = "John makes Mary go." ii. John ga Mary ni John nom Mary dative

hon ο yom-sase-ru. book acc read-cause-tense = "John

makes Mary read the book." We analyze, e.g., (80c, i) and (80c, ii) as having the basic structures shown respectively in (81a,b)

20

Let us concentrate on (81b).' The relevant point is that the immigrant 2 arc, B, does not overrun its neighboring 2 arc, D. Thereasonis that D locally sponsors, and is locally assassinated by, E , and E locally sponsors B . Thus, in keeping with the coordinate determination laws, (D), (E) and (B). Thisstateofaffairsisa function of universal principles, which we now make explicit. A central aspect of our analysis of clause union constructions, adapted from stage 2 RG, is the view that the verb of the downstairs clause is the head of a

20

The "incorporation" of the verb which P-heads the U arc into the verb which P-heads the neighboring P arc, i.e., the realization of the two verbs as a single word (either single lexical item, or compound) is a common but nonuniversal feature of clause union constructions. It is found in Turkish and Japanese but not French, Italian, or Spanish clause union constructions of the productive varie­ ty. This language-particular aspect of clause union constructions is largely ignored in the following discussion.

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

325

(81) a.

sase-ru

John (go)

Mary(o)

ik

b,

John (go)

Mary(ni) ®/

yom hon (o)

U arc which is a neighbor of the upstairs P arc, whose head "triggers" clause union or verb raising (one such trigger in Japanese being sase "cause"). The most fundamental characteristic of such constructions is

326

8. CHO ARCS

the "collapsing" of two clauses into one. Particular to APG are the sponsor and erase pairs shown in, e.g., (81b). In addition to the mere presence of a U arc, clause union construc­ tions are analyzed in APG terms as involving a set of universally restrict­ ed sponsor and erase pairs. For instance, in (81b), given the occurrence of U arc E , all of the following, are, inter alia, determined by PN laws: Local Sponsor (D, E), Erase(E, D), LocalSponsor(E j C), Local Sponsor(E, B), Foreign Successor(C, H), Erase(C,H), Foreign Successor (Β, I), Erase(B,I), Foreign Successor (E, J), Erase(E1J). In addition, that D is a self-sponsoring, Nuclear Term arc, J is a P arc, and E is the neighbor of a P arc are all universally determined. That is, we impose PN laws to insure, inter alia, the following:

r\ι

(82) a. U arcs are foreign successors of P arcs. b. U arcs erase their foreign predecessors. c. U arcs are neighbors of P arcs. d. U arcs erase their local sponsors. e. Local sponsors of U arcs are self-sponsoring, Nuclear Term arcs. f. The predecessor of a U arc is a branch of the local sponsor of that U arc. The claimed universal regularities in (82) are guaranteed by the following: (83) PN Law 66 (The U Arc Foreign Successor Law) U arc (A) -» (3B) (Foreign Successor (Α, Β)Λ P arc (B) Λ Erase (A, B)).

(84) PN Law 67 (The U Arc Local Sponsor Law) U arc (A) λ Local Sponsor (B, A) -> Nuclear Term arc (B) λ Self-Sponsor (B) λ Erase (A, B) .

21 (82c, e) are incompatible with the speculation in Chapter 7, note 18, that nominalizations might involve U arcs. If that conjecture is supported by future research, this aspect of the current treatment of U arcs will have to be altered.

8.6 . CLAUSE UNIONS AND THE CHOMEUR LAW

327

(85) PN Law 68 (The U Arc Predecessor Branch Law) U arc (A) Λ Successor (Α, Β)

Λ

Local Sponsor (C, A) H> Branch (B, C) .

Of course, since all of PN laws 66-68 have essentially the same ante­ cedent, they could be combined into a single more elegant statement: U arc (A) -» (3B) (Foreign Successor (Α, Β) Λ P arc (B) Λ

(86)

(Local Sponsor (C, A) -> Nuclear Term arc (C) Λ Self-Sponsor (C) Λ Branch (Β, C))) Λ (Sponsor (D, A) -» Erase (A, D)) . This formulation has the virtue, besides its compactness, of bringing out the generalization that U arcs erase all of their sponsors. The U Arc Foreign Successor Law guarantees (82a,b); The U Arc Sponsor Law (82d,e); and The U Arc Predecessor Branch Law (82f). (82c) is a theorem of The U Arc Local Sponsor Law and independent assumptions: (87) THEOREM 71 (The U Arc P Arc Neighbor Theorem)

U arc (A) - (3B)(P arc (B) Λ Neighbor {k, B)) . Proof. Suppose A' is a U arc. Then, it follows from PN law 67, The U Arc Local Sponsor Law, that there is some Nuclear Term arc, B', which is a neighbor of A'. From PN law 52, The Central Arc Tail Law, and PN law 35, The Basic Clause Predication Law, it follows that there is some P arc neighbor of B', which is necessarily also a neighbor of A'. QED. All U arcs invariably erase two arcs: their P arc foreign predeces­ sors, in accordance with PN law 66, and their local sponsors, in accord­ ance with PN law 67. More specifically, U arcs unhook their foreign predecessors and zero their local sponsors. These circumstances are con­ sistent with PN law 9, The Multiple Assassin Law, stated in Chapter 5, which limited the number of arcs a given arc can zero to exactly one. 22

r\ Λ

Arcs zeroed by U arcs are always their local sponsors. Hence, this type of zeroing pair is irrelevant to PN law 76, The Nominal Arc Zeroing Law, dis­ cussed in Chapter 9. This requires that arcs zeroed by arcs they do not sponsor must have heads which are members of the class Inexplicit. Heads of local spon­ sors of U arcs are invariably not members of this set. Thus, the condition of nonsponsorship in this law, inter alia, maintains consistency with our treatment of clause union constructions.

328

8. CHO ARCS

Although (84)-(87) do not provide a full-fledged theory of clause union constructions, they do place severe constraints on them. Given that a PN has a U arc, it must have a subpart of the form:

(88)

GRx = ! or 2

GRx

b α So far missing from the formal description is an account of the arcs which are, roughly, colimbs of D, and their foreign successors, if any. For example, returning to (81b), we have yet to specify anything about arcs H , I, B, and C. Part of what we wish to specify formally is which colimbs of a U arc predecessor must have foreign successors local­ ly sponsored by that U arc. We call such arcs, e.g., H and I in (81b), launchers. Before we can further characterize this, and other related aspects of these constructions, it is necessary to define precisely which arcs like H and I in (81b) are relevant. In (81b), all and only the colimbs of J which are riot locally erased are of relevance to the problem at hand. The class of arcs which are not locally erased is important (see the definition of "Shallow Arc" in (12.10)), and we take this opportunity to introduce the following: (89) Def. 142: Output arc (A) (3C) (Foreign Successor (C, Α) Λ Local Sponsor (B, C)) .

335

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

PN law 69 states that if an arc is a launcher with respect to B, then it has a foreign successor locally sponsored by B. Since H in (96a) and J in (96b) are not launchers, they do not come under the scope of The Launcher Law and are not required to have foreign successors locally sponsored by the relevant U arcs. In contrast, G in (81a) and H and I in (81b) are launchers and hence are required, as desired, to have foreign successors locally sponsored by the relevant U arcs. As stated, PN law 69 would not prevent a launcher from having a replacer since it does not force the foreign successor of a launcher to erase its predecessor. However, there is no reason to believe that launchers can have replacers. This could be built into PN law 69 easily enough, but has not been since, more generally, there is no reason to allow any potential launchers to have replacers. Hence, we impose the more general stricture: (99) PN Law 70 (The Potential Launcher Erasure Law) Potential Launcher (Α, Β) λ Foreign Successor (C, A) -» Erase (C, A) . PN law 70 insures that, e.g., B erases G in (81a), B erases I and C erases H in (81b), and C erases H and B erases J in (96b), even though J in (96b) is not a launcher. More generally, every neighbor of a U arc predecessor is erased: (100) THEOREM 73 (The U Arc Foreign Erasure Theorem) U arc (A)

Λ Foreign

Successor (Α, Β)

Λ Neighbor (B,

C) -->

(3D) (Erase (D, C)) . Proof. Suppose that A' is a U arc foreign successor of B'. Consider an

arbitrary neighbor of B', C'. If C' is a potential launcher with respect to A', then it follows from The Potential Launcher Erasure Law that C' is erased. Suppose that C' is not a potential launcher with respect to C'. If C' = B', then The U Arc Foreign Successor Law determines that C' is erased (by A'). Hence, assume that C^B'. Then, C' is a colimb of B',

336

8. CHO ARCS

the predecessor of U arc A'. Since C' is, by hypothesis, not a poten­ tial launcher, the definition of "Potential Launcher" guarantees that C' must not be persistent at the tail of B'. Clearly, the tail of B' is the point of a constituent, Q. It then follows from the definition of "Persis­ tent" that there is some arc in Q which erases C'. This exhausts all possibilities. QED. Theorem 73, in conjunction with The Overmined Arc Erase Law of Chapter 9, insures that none of the arcs in the complement of a clause union con­ struction are surface arcs. An L-graph clause whose P arc is the foreign predecessor of a U arc is never an S-graph clause. Thus, the S-graph of a clause union construction has at least one less clause constituent than its L-graph has. Several further observations are in order about (96b). First, clause 9 with verb suele "tend," like its English counterpart (see (7.83) repeated below), is analyzed as an initial unaccusative clause. Second, immigrant arc B is, under our analysis, a 2 arc. Third, B overruns D, its local sponsor, at c 2 . However, since the employed C2 U arc E locally assassinates D , the conditions for the introduction of a Cho arc are not created. This is important, since it highlights the nonderivational char­ acter of the APG treatment of clause union constructions in particular and the nonderivational nature of PNs in general. Thus, a structure involving just raising and not clause union would require the occurrence of a Cho arc: 55

(7.83)

tends

Melvin

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

337

This provides a different sort of illustration of how the APG treatment of clause union constructions and The Chomeur Law prevent undesirable occurrences of Cho arcs. Further, in (96b) C overruns B at C 3 . But since B is the local predecessor of A, no Cho arc successor of B is required. Fourth, (96b) provides an illustration of an immigrant arc, E, being the local sponsor of another immigrant arc, e.g., C. Since E is not locally assassinated, it falls through from C2 to C 3 . Finally, although (96b) involves raising, "unaccusative advancement" (the pair Sponsor (B, A)), and clause union, it has the same number of strata as PNs which are structurally parallel in relevant aspects, except for not involving raising and "unaccusative advancement." For example, (81) and (82), which do not involve raising and "unaccusative advancement," also have three strata, because raising and "unaccusative advancement," in conjunction with clause union, do not add extra strata. This is a result of the fact that in (96b) the first coordinate of the immigrant unaccusative arc, B , associated with raising, is the same as the first coordinate of the immigrant U arc, E, associated with the clause union aspects of the sentence, while the first coordinate index of C , the arc locally sponsored by E , is +1 of the first coordi­ nate index of E. Raising, "unaccusative advancement," and clause union "occur simultaneously" in (96b) without causing problems. This further exemplifies the nonderivational characteristics of APG sentence structures. There is another, apparently universal, aspect of clause union con­ structions, much discussed in the literature, which we have not yet touched on. In earlier, informal RG terms, this is the issue of what relation the dependents of the complement clause in the clause union construction bear upstairs (see Aissen and Perlmutter [1976], Cole and Sridhar [1976], Comrie [1974b, 1976], and Postal [1977] for discussion). 24 To be more

24

The view of this matter developed below is not shared by all researchers. For different analyses, cf. Comrie (1974b, 1976) and Cole and Sridhar (1976). We lack space here to deal with these opposing viewpoints.

338

8. CHO ARCS

concrete and slightly more formal, the question is what R-signs arcs like B in (81a), B and C in (81b), B in (96a), and C in (96b) should have. We adopt in essence the claim of RG work by Perlmutter and Postal that in such constructions a downstairs ergative 1 "becomes" an upstairs 3, and a downstairs absolutive "becomes" an upstairs 2. Postal (1977) states this view as follows: In these constructions, which involve a kind of compression of a main and subordinate clause into one superficial clause, comple­ ments behave differently according to whether they are ultimately transitive or not: (5) a Pierre travaille. Peter works

b J'ai fait travailler I have made work "I had Peter work"

J Pierre 1 t*a Pierre J . to

c Pierre ecrit la chanson. "Peter writes the song" d J'ai fait ecrire la chanson "I had Peter write the song"

i*Pierre I ( a Pierre/ '

The chief superficial difference is that, in these constructions, the subject of an intransitive complement shows up without preposition, as does the direct object of a transitive clause. But the subject of a transitive clause is marked with the preposition a . The deeper generalization, which I lack space to discuss, is that an ultimately ergative (in the sense of (3) above) nominal of a transitive comple­ ment clause is assigned as indirect object of the resulting main clause, while an ultimately absolutive (in the sense of (3)) nominal of the complement is assigned as direct object of the main clause. Moreover, these relationally expressed generalizations, which dif­ ferentiate transitive clause subjects from other nuclear terms, are by no means particular to French, but can be claimed to be uni­ versal laws.

However, the dependents of such complements can clearly be other than just ergative and absolutive NPs, i.e., other than nuclear terms. Thus, there remains the question of what happens to nonnuclear terms. The stage 2 RG answer to this question was that all such dependents become "dead" dependents upstairs. In APG terms, such dependents are the heads of upstairs arcs with the R-sign Dead. 25 25

In earlier RG work, the verb analyzed here as corresponding to the head of a U arc was referred to as a dead verb. This usage is confusing, given the cur­ rent use of Dead as an R-sign defining a subclass of Central arcs, and it is avoid­ ed in the current work.

339

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

To illustrate, consider the following French examples: (101) a. Marie a

fait donner a Jeanne Ie livre a Claude.

Marie had made give

to Jeanne the book to Claude =

"Marie had Jeanne give the book to Claude." b. Marie a

fait repondre Jacques a Jeanne.

Mariehadmade answer

Jack

to Jeanne =

"Marie had Jack answer Jeanne." These involve complements with output 3 arcs. In terms of the above assumption, CIaade in both (101a,b) is a dead dependent of the upstairs clause. In contrast, Jeanne in (101a) is a 3 upstairs. In present terms, partial analyses of (101a) would be (102) and (103) respectively.

(102)

Dead C|C2C3

(a) fait

(b) Claude Marie

Ie livre donner

(a) Jeanne

In (102), the downstairs 3 arc, I, is the foreign predecessor of an up­ stairs Dead arc, D, while the downstairs ergative arc, K , is the foreign

340

8. CHO ARCS

(103)

Oeod/c

(α) fail

Marie (a) Jeanne

repondre

Jaqques

predecessor of an upstairs 3 arc, B . In (103), the downstairs 3 arc, H , is the foreign predecessor of the upstairs Dead arc, C . This is all in accord with the informal observations above. Since, e.g., the heads of arcs B and D in (102) look formally simi­ lar, i.e., they both look superficially like 3s, one might wonder what justification there is for assigning these arcs different R-signs as done in (102). While we cannot, in this volume, deal with this complex area in detail, it is worth mentioning one piece of evidence in favor of the view that, e.g., D in (102) is a Dead arc rather than a 3 arc. Nominals like that corresponding to the heads of 3 arcs like D in (102) and C in (103) cannot determine Dative clitics, unlike heads of true 3 arcs like B in

(102) and the standard 3 arc head in the PN of (104a):

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

(104) a. Marie

Iui

341

a donne Ie livre.

Marie to him has given the book = "Marie gave him the book." b. Marie

Iui

a fait donner Ie livre a Claude.

Marie to him has made give the book to Claude = "Marie had him give the book to Claude" (*"Marie had Claude give the book to him"). c. *Marie

Iui

a fait

repondre Jacques.

Marie to him had made answer Jacques. Accepting then the above claim that nonnuclear terms are "assigned" the status dead upstairs in such constructions, the problem arises as to how to formally specify the claims concerning nominal "reassignment" in these cases. In APG terms, the answer is to specify, via a PN law, the R-Sign associated with foreign successors of launchers. We have de­ veloped all of the theoretical machinery needed for this. The basic state­ ments needed are: (105) a. If a launcher is C£^ na j ergative, its foreign successor is a 3 arc. b. If a launcher is cjj na j absolutive, its foreign successor is a 2 arc. c. If a launcher is not a Nuclear Term arc, its foreign successor is a Dead arc. While launchers are output arcs, i.e., all foreign predecessors relevant to (105) are output arcs, the generalizations stated in (105) refer to the iinal stratum of the relevant stratal family. Hence, nonoutput arcs can in­ fluence the "assignment" effected by (105). For example, suppose the clause with the launchers had a final 2 arc which self-erased. This 2 arc would not be an output arc, hence would not be a launcher, and so would not itself figure in the "assignment" effected by (105). However, this final, nonoutput arc would affect the assignment of the output 1 arc. The output 1 arc would, under such circumstances, be treated by (105) as an

342

8. CHO ARCS

ergative, rather than as an absolutive, arc. Since (105) refers just to out­ put arcs, more precisely, to those which are launchers, final stratum arcs which are not launchers will not come under the scope of (105), as desired. If nonlaunchers were affected by (105), inconsistencies would result. For example, consider (96b), which involves both raising and clause union. If J were erroneously affected by (105) (supposing the "launcher conjunct" were dropped), i.e., if it were "forced" to be the foreign prede­ cessor of a 3 arc, as well as the predecessor of the 2 arc defining rais­ ing, then The Successor Uniqueness Theorem would be contradicted. Postal (1977) presents evidence to support the view adopted here to the effect that final stratum nonoutput arcs are relevant to the "assign­ ment" of the R-signs associated with the foreign successors of launchers. The general hypothesis can be clarified by appeal to an artificial example. Suppose that (106a) with structure (106b) were embedded in a causative clause union structure, as shown in (107): (106) a. Melvin ate. b.

Melvin

ate

UN

(107) a. John made Melvin eat. b.

Melvin

UN

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

343

We are assuming for discursive purposes that (106) does not involve, e.g., antipassivization and, hence, Metvin in (106) is the P-head of a final stratum ergative arc, A . The output arcs associated with (106b) are A and B . C is a final, nonoutput arc. Thus, C is not a launcher. It therefore cannot have a foreign successor and so is irrelevant to PN law 69. According to the hypothesis of Postal (1977), as translated into APG terms, if (106b) is embedded as part of a clause union construction not in­ volving raising or equi, A should be the foreign predecessor of a 3 arc, via (105), as illustrated in (107b). Mutatis mutandis, (106b) seems to be the correct analysis for so-called unspecified object (UO) clauses in Basque. Postal (1977) points out that the analysis in Basque of UO clauses as involving final stratum 2s "auto­ matically" accounts for the fact that such clauses have three properties characteristic of transitive clauses: For there are languages in which UO clauses betray fairly unmistakeable evidence of having direct objects, even though, just as in (6e), no object is visible. Basque, as described by Lafitte (1962), is such a language, as noted by Comrie (1972: 246). Transi­ tive clauses in Basque have at least three notable peculiarities. There is (i) an auxiliary verb, ukan "have" and its many inflec­ tions particular to such clauses, contrasting with the auxiliary izan "be" and its many inflections found with intransitive clauses; (ii) ergative case marking, so that the subject of a transitive clause is marked ergative, while the subject of an intransitive is in the absolutive; (iii) an ergative- absolutive pattern of agreement of inflected verbs (including auxiliary) with nuclear nominals. Strikingly, UO clauses have all three properties typical of transi­ tive clauses, as seen by comparing (9c) with (9a,b) (du in (9a,c) is a transitive auxiliary manifesting ergative agreement with the third person singular ergative nominal Piarresek): (9)

Basque (from Lafitte [1962: 44,47,46,342]) a Paulok Piarres maite du Transitive Clause Paul„ ,. Peter., , . like has = "Paul likes Peter" Ergative Absolutive b Piarres Peter Absolutive

hil da Intransitive Clause die is = "Peter died"

c Piarresek Peter r , Ergative

maitatu du UO clause love has = "Peter has liked/loved"

d Piarresek egin du etchea Transitive Clause Peter r , make has house., . = "Peter made the Ergative Absolutive house"

344

8. CHO ARCS

e

Piarresek egina da etchea Passive Clause Peter_ . make, ,. . , . is house., . .. Ergative (participle) Absolutive = "The house was made by Peter"

Observe that the passive clause (9e) corresponding to (9d) has, as predicted by the detransitivizing character of Passive discussed in Section 2, the intransitive auxiliary, indicating that Basque aux­ iliary choice is not regularly determined by early levels of structure. Thus any universal principle claiming that UO clauses are neces­ sarily functionally intransitive, motivated by cases like French (6e) or Japanese (7e), would evidently make false predictions about Basque as described in Lafitte (1962). Furthermore, support for the hypothesis that final, nonoutptit, arcs in­ fluence the R-Sign of the foreign successors of launchers comes from Mangyan where UO clauses behave transitively when embedded as comple­ ments of causative constructions, as observed by Postal: 26 More impressive evidence of the failure of mere invisibility to detransitivize UO clauses could derive from cases analogous to the "verb raising" constructions in French, if there were languages where UO clauses function transitively in such situations. Data from the Philippine language Mangyan, given in (11), kindly brought to my attention by Sarah Bell, seem to indicate that there are such languages: (11)

Mangyan (from Gardner and Maliwang(1943)) a Ako [umuli] sitay pagbalay Intransitive Clause I [active-stop] at house = "I'll stop at this house" b Si Maria [mag pa turog] anak Causative of Intr. Cl. Maria [active-cause-sleep] child = "Marie is putting the Nominative baby to sleep" c Si Maria

[magugas] mangapinggan Transitive Clause [active-washed] dishes = "Maria washed the dishes"

d Ako nagpapaugas pinggan kan Maria Causative of Tr. Cl. I [active-cause-wash] dishes to = "I order Maria to wash the dishes" e Siya [nagpakikihampang] kan Pedro Indirect Object Clause he [active-speaks] to Pedro f Ti anak [sumurat] Unspecified Object Clause the child [writes] ^D. Perlmutter informs us that there are dialects of Paraguayan Spanish where UO clauses act transitively in causative clause union constructions.

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

g Ti pari [magpabasa] sa manga anak the priest [active-cause-read] to plural child = "The priest asked the boys to read"

345

Causative of Unspecified Object Clause

Like other Philippine languages, Mangyan has case-marking particles to mark superficial clausal grammatical relations (as argued effectively for Cebuano in Bell (1976)). Subjects are marked with si if personal names, with ti otherwise. Direct objects are optionally preceded by si or ti. Indirect objects and locatives take kan if proper names and sa otherwise. There is a causative con­ struction, relationally parallel to that in French, except that, as in Japanese, the causative element is an affix. In a causative, an ordinary intransitive subject shows up as direct object, cf. (11a,b), while an ordinary transitive clause sub­ ject shows up looking like an indirect object marked with kan, com­ pare (lld,e). This is, as expected, parallel to French and Japanese. However, in the causative of a UO clause, the complement subject shows up looking like, and I suggest it in fact is, an indirect ob­ ject, marked with sa, cf. (Hg). Thus UO clauses appear to behave transitively, not intransitively, in Mangyan causatives, in this re­ spect contrasting with analogous clauses in French and Japanese. Although the available data is quite sparse, this genuinely suggests that the intransitive properties of French UO clauses must, in cross-linguistic perspective, be due to something independent of object invisibility. This follows since this property is shared by Mangyan, in whose causative construction, however, UO clauses are apparently functionally transitive. However, as Postal (1977) discusses at length, there are many cases where final Is of UO clauses like A in (106) behave intransitively. Under the assumptions of Postal (1977) and those adopted here, such cases are analyzed as involving antipassive (see Chapter 7) and hence the final 1 arcs are not final ergative arcs.

07

27 An a priori possible alternative to Postal's antipassivization analysis for final stratum intransitive UO clauses, namely, one where the initial 2 arc is the local predecessor of a 3 arc (so-called direct object retreat), is impossible under current assumptions. As discussed in detail in Chapter 9, UN nodes cannot, in general (see PN law 79) be the heads of two distinct arcs. Under the direct object retreat analysis, however, this would be required. (i)

Melvin

ate

UN

346

8. CHO ARCS

(105) is an informal statement of the regularities claimed to govern the R-signs of foreign successors of launchers. The following embeds the claims of (105) in the APG formalism: (108) PN Law 71 (The Launcher Successor R-Sign Law) Launcher(A) a Successor (B, A) -» ((Ergative (A, C£inaj(b)) -» 3 arc (B)) λ (Absolutive(A, C£j na j (b)) -> 2 arc (B)) λ (Not(Nuclear Term arc(A)) -» Dead(B))) . The Launcher Successor R-Sign Law thus insures that the (foreign) suc­ cessor of a launcher is either a 3 arc, a 2 arc, or a Dead arc, depending, respectively, on whether the launcher is a final ergative arc, a final absolutive arc, or a final nonTerm arc.28 Dead arcs play a highly restricted role in APG. As pointed out in Chapter 10, note 20, it is a theorem that every Dead arc graft is a replacer. On the other hand, every organic Dead arc must have a Central arc foreign predecessor and a U arc local sponsor. These restrictions are guaranteed by the following:

In contrast, the antipassivization analysis circumvents this problem, since the UN arc is zeroed by the 2 arc successor of the X arc: (ii)

UN

ate

In both (i) and (ii), A is a Cj ergative arc and a CfJ na J unergative arc, so the clauses are in both cases intransitive in the final stratum. But (i) violates PN law 79, since UN is the head of both B and C . 28 The claim in PN law 71 that all nonNuclear Term arc launchers have Dead arc successors may well be incorrect in tile case of Oblique arc launchers. Possi­ bly, the proper principle for these arcs is that a launcher which is an Oblique arc of type X (Ben, Loc, etc.) has a successor which is also of type X . Certain evidence bearing on this involving the choice of voice markers in Phillipine lan­ guages is discussed in Bell and Perlmutter (to appear).

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

347

(109) PN Law 72 (The Dead Arc Foreign Successor Law) Dead arc (A) a Organic(A) -> (ΉΒ) (Foreign Successor (A, B) a Central (B)) . (110) PN Law 73 (The Dead Arc Local Sponsor Law) Dead aic(A) λ Organic(A) a Local Sponsor (B, A) -» U arc(B) . Thus, all organic Dead arcs are immigrant arcs of a restricted type. This characterization of organic Dead arcs permits, with the addition of The Core Arc Local Successor Law, stated below, a proof that em­ ployed local successors of Core arcs are either P arcs or Term arcs. (111) PN Law 74 (The Core Arc Local Successor Law) Core arc (A) a Local Successor (Β, A) λ Not (P arc (B)) -> Central ate (B) . This law restricts nonP arc local successors of Core arcs to Central arcs. The third conjunct is required because of our treatment of predicate nominals in Chapter 7, section 4. (112) THEOREM 74 (The Core Arc Local Successor Theorem)

Core arc (A) a Local Successor(B, A) a Employed(B) a Not( P arc (B)) -» Term arc(JS) . Proof. Suppose A' is a Core arc with employed local successor B',

which is not a P arc. The Core Arc Local Successor Law determines that B' is a Central arc. Hence, B' is either a Term arc, an Oblique arc, or a Derivative arc. It follows from The No Oblique Successor Law that B' cannot be an Oblique arc. Further, PN law 72 guarantees that B' cannot be a Dead arc, since this law insures that all organic Dead arcs are immigrants and hence not local successors. Thus, since B' is, by assumption, employed, it cannot be a Derivative arc. Therefore, B' is a Term arc, QED. Thus, from Theorem 74, we know that local successors of Core arcs are either Cho arcs, P arcs, as in our analysis of predicate nominal construc­ tions, or Term arcs.

348

8. CHO ARCS The restricted role of Dead arcs is further highlighted by the fact that

they cannot be self-sponsoring and, hence, cannot be logical arcs. These properties are shared by Cho arcs and U arcs. Below we present the theorems which, in conjunction with Theorem 62, The Cho Arc NonselfSponsoring Theorem, support these observations: (113) THEOREM 75 (The Dead Arc Nonself-Sponsoring Theorem) Deadarc(A) -> Not (Self Sponsor (A)) . Proof. Suppose A' is a Dead arc but, contrary to the consequent, is selfsponsoring. Therefore, A' is organic. Thus it follows from PN law 72, The Dead Arc Foreign Successor Law, and the irreflexivity of the Succes­ sor relation that A' is sponsored by some distinct arc. Hence, PN law 4, The Self-Sponsor Law, determines that A' cannot be self-sponsoring. QED. (114) THEOREM 76 (The Dead Arc Nonlogical Arc Theorem) Dead Arc (A) > Not (Logical arc (A)) . Proof. Suppose A' is a Dead arc. Theorem 75 shows that A' is not self-sponsoring. Hence, A' cannot be a logical arc since these are selfsponsoring by definition. QED. (115) THEOREM 77 (The Cho Arc Nonlogical Arc Theorem) Cho arc (A) -> Not (Logical arc (A)) . Proof. Suppose A' is a Cho arc. It follows from Theorem 62, The Cho Arc Nonself-Sponsoring Theorem, that A' is not self-sponsoring. Hence, from the definition of "Logical Arc," A' cannot be a logical arc. QED. (116) THEOREM 78 (The U Arc Nonself-Sponsoring Theorem) U arc (A) -» Not (Self-Sponsor (A)) . Proof. Suppose A' is a U arc. Then, PN law 66, TheU Arc Foreign Successor Law, and the irreflexivity of Successor require that some dis­ tinct arc sponsor A'. Hence, PN law 4, The Self-SponsorLaw, guaran­ tees that A' is not self-sponsoring. QED.

8. 6 . CLAUSE UNIONS AND THE CHOMEUR LAW

349

(117) THEOREM 79 (The U Arc Nonlogical Theorem) U arc (A) -> Not (Logical Arc(A)) . Proof. Suppose A' is a U arc. Theorem 78 shows A' is not selfsponsoring. Hence, by the definition of "Logical Arc," A' is not a logi­ cal arc. QED. We turn briefly to a different topic which interacts with our treatment of Cho arcs and clause union constructions. The class of verbs which P-head P arc neighbors of U arcs, i.e., the upstairs "trigger" verbs of clause union constructions, can be conveniently divided into two sub­ groups: (i) regular clause union triggers, e.g., Spanish hacer and Japanese sase (see (81)) and (ii) equi clause union triggers, which have two sub­ divisions: (a) raising clause union triggers, e.g., Spanish suele (see (96b)) and (b) "true" equi clause union triggers, e.g., Spanish quiere (see (96a)). We refer to all such elements as unionizers. (118) Def. 146: Uniomzer(a) *-* (3B)(3C)(P arc(B)AU arc(C)A Neighbor (B, C) λ Head (a, B)) . A fact observed but not explained by Aissen and Perlmutter(1976) is that unionizers which occur in clause union constructions with raising triggers do not also occur in regular clause union constructions. In Span­ ish, there are no clause union analogues to (96b) without raising. We sug­ gest that raising is a necessary concommitant of clause union constructions whose unionizers are P-headed by verbs like suele because of The Nuclear Term Arc Stratal Continuity Law, mentioned briefly in Chapter 7: (119) PN Law 47 (The Nuclear Term Arc Stratal Continuity Law) Cjth Stratum (b) e Stratal Family (b) λ Point (b, Q) λ Basic Cl Constituent(Q)

(3A)(Nuclear Term arc(A) λ

Aecjth Stratum (b)) . PN law 47 insures that every stratum of every basic clause of any given PN contains at least one Nuclear Term arc. A key point here is that all

350

8. CHO ARCS

of the verbs with raising unionizers take initial unaccusative complements. Thus, a PN exactly like (96b), except that raising was not involved, would look like: 9

(120)

suele

comer Luis

In (120), I's foreign successor is the 3 arc B, locallysponsoredby E, in accord with PN laws previously formulated. The significant property of (120) for present purposes is that the only arcs in the c 2 nd stratum (9) are E and G. The C2 NuclearTerm arc Tequired j by PN law 47 is missing. Hence, (120) is ill-formed. Under current APG assumptions, clause union constructions ate then only possible with unionizers like suele if the construction is also a raising construction. There cannot in principle be regular clause union analogues of examples like (96b). The existence of raising clause union constructions with initial un­ accusative complements raises the question whether there can be raising clause union constructions with initial accusative complements. We know of no such cases and assume that PNs of the following form are ill-formed in all languages:

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

351

(121) a.

Cho/c

d

b.

In (121a) the local sponsor of U arc G is the accusative arc E. The 2 arc launcher 1 is the foreign predecessor of the 2 arc D, which over­ runs at C3 the raising successor C. C, in accord with The Chortieur Law, sponsors Cho arc successor B. In (121b), accusative arc G locally

352

8. CHO ARCS

sponsors U arc H , and E, the foreign successor of launcher J , overruns at c 3 the raising successor 2 arc D. D locally sponsors the 1 arc C,

avoiding the necessity of Cho arc introduction. C and B co-

sponsor Cho arc A. The relevant formal feature which (121a,b) share is that in both an immigrant arc overruns some arc (D overruns C in (121a) and E overruns D in (121b)). Our current claim is that such overrunning is highly restricted. Except for one small class of exceptions, it appears that an immigrant can only overrun its local sponsor.

(96b), however, provides an

exception to the above statement. There, immigrant arc C overruns B at c 3 with no resulting ill-formedness, but B does not locally sponsor C. The relevant formal difference between cases like (96b) and those like (121a,b) seems to be this: in the former, the arc overrun at c k + 1 an immigrant it does not locally sponsor is unaccusative at the latter, the arcs overrun at sponsor are accusative

at

by

while in

by immigrants they do not locally This suggests the following generalization:

(122) An immigrant arc can overrun an arc, A , other than its local sponsor at

only if A is unaccusative at

Formally: (123) PN Law 75 (The Immigrant Overrun Law) Immigrant (A) Not (Sponsor (B, A))

Tail(b, B) (Unaccusative

This PN law permits, e.g., immigrant arc C in (96b) to overrun B at c 3 , even though B does not sponsor C , since B is unaccusative at c 2 . However, PN law 75 blocks (121a,b), since the arcs c k+1 -overrun by immigrants, C and D, are accusative at c^. It follows from PN law 75 that there cannot be, in a given clause, two 3 arc foreign successors of Gen arcs. Schematically, (124) is blocked:

8. 6 . CLAUSE UNIONS AND THE CHOMEUR LAW

353

b In (124) both B and D are immigrant 3 arcs. D, in violation of PN law 75, overruns B , which is not its local sponsor and not unaccusative at any stratum. Another consequence of PN law 75 is that in clause union construc­ tions, a 3 arc foreign successor of a launcher (a "clause union" 3 arc) cannot assassinate a 3 arc local successor or cosponsor a Cho arc suc­ cessor of an arc in the upstairs clause. From this, one can predict that, e.g., in Georgian clause union constructions a "clause union" 3 arc can­ not cosponsor a Cho arc successor of a domestic 3 arc in the upstairs clause. A priori, this might happen in sentences involving regular clause union constructions, where the complement is transitive (hence has a 3 arc potential launcher) and is in the evidential mode which requires inver­ sion (see Harris [1976,1977]). Such sentences do exist in Georgian, as the following examples from Harris (1976) show. Compare (125), which is a regular clause union construction in the present tense indicative with transitive complement, and (126), which is a regular clause union con­ struction with a transitive complement coupled with inversion, since the sentence is in the evidential mode. Assuming Harris's (1976) analysis of (126), it would have, in present terms, the basic structure (127).

354

8. CHO ARCS

(125) mascavlebeli teacher-NOM

atargmninebs

mocapes

he-causes-translate-him-it

pupil-DAT

axal gakvetils new lesson-DAT "The teacher has the pupil translate a new lesson." (126) mascavlebels teacher-DAT mocapis

mier.

pupil

by

gadautargmninebia

axali

gakvetili

he-caused-translate-it

new

lesson-NOM

"The teacher apparently had the pupil translate a new lesson.' (127)

cause

axali gakvetili

I

translate mocapis mier mascavlebels

PN law 75 blocks PNs like the following:

355

8.6. CLAUSE UNIONS AND THE CHOMEUR LAW

Cho

cause

new lessons

translate teacher pupil

The significant difference between (127) and (128) is that in the form­ er, the domestic 3 arc B overruns at c 4 the immigrant 3 arc D , while in the latter, the immigrant 3 arc D overruns at C 3 the domestic 3 arc B. The latter situation violates PN law 75, since B neither sponsors D nor is unaccusative at c 2 · We judge from the description in Harris (1976) that structures like (128) are impossible in Georgian. Moreover, we know of no such structures in any other language. Thus, PN law 75 blocks a number of apparently unattested PNs. To conclude, within the current framework, most aspects of clause union constructions can be formally specified in terms of PN laws, with very little left to rules of individual grammars. In particular, grammars of individual languages must specify in essence which verbs must or must

356

8. CHO ARCS

not P-head (i) U arcs and (ii) P arc neighbors of U arcs. Other re­ stricting conditions, nonuniversal in nature, such as whether the down­ stairs clause must be intransitive, whether raising or equi is impossible or mandatory, and whether the U arc head must be incorporated into the verb of its neighboring P arc, are left to the grammars of particular lan­ guages. Finally, the PN laws governing clause union constructions inter­ act in such a way as to prevent undesirable occurrences of Cho arcs.

8.7. Postscript 1: Partially alternative views of Cho arcs Earlier, we justified several weakenings of the RG view of chomage, arriving at PN law 62, The Chomeur Law. On further contemplation, it has occurred to us that there is an alternative view of chomage, which, while having the same basic set of entailments, is more elegant. This conception would involve a further weakening of The Chomeur Law, name­ ly, the abandonment of that part of the law which insures that a cj^-Overrun arc not locally assassinated by a Cj c employed arc has a Cj c Cho arc successor (the left-to-right part of (57) above). The Motivated Chomage aspect of The Chomeur Law, however, would be retained (the right-to-left part of (57)), with some simplification: (129) Motivated Chomage Cho arc (A) λ < Cj i β > (A) λ Successor (A,B) -» (3C) (Cj t -Overrun(C i B)) . Abandonment of all but the motivated chomage part of The Chomeur Law would also necessitate taking stratal uniqueness as a law, since the proof of Theorem 55, The Stratal Uniqueness Theorem, depended on the left-to-right part of The Chomeur Law: (130) Stratal Uniqueness Term x arc (Α λ Β) λ cj^(A λ Β) -> A = B . However, this does not really cost anything, since PN law 48, The Earliest Strata Uniqueness Law, would then be dropped.

8.7. ALTERNATIVE VIEWS OF CHO ARCS

357

This conception would thus involve a return to the "traditional" RG position of postulating stratal uniqueness as a law, but a further differ­ entiation from the "traditional" RG view of chomage. The basic princi­ ples specifically governing chomage would then be (129) and PN law 63, The Cho Arc No Local Successor Law. PN law 50, The Demotion No Replacer Law, while not specifically mentioning Cho arcs, would also re­ main relevant to controlling their distribution. We would also have to give up or reprove some theorems, e.g., Theorem 68. We leave this to future research.

8.8. Postscript 2: The sponsors of domestic Cho arcs A feature of the conception of domestic Cho arcs proposed in this chapter is that each such arc is cosponsored, one sponsor being the pred­ ecessor, the other the overrunner of the predecessor. This view is elabo­ rated in section 2. This idea dates to the beginning of our work on the APG conception of Cho arcs. At that time, it appeared strongly motivated. However, the strongest motivation for this view disappeared as we refined our conception of PN (and, in particular, revised our definition of 'PN' by imposing the PN Sponsor Condition and our conception of ghost arc [see Chapter 10]). As a consequence, the idea that domestic Cho arcs have two sponsors is not currently strongly motivated and, on reflection, we are now inclined to view this as an unfortunate mistake, which has certain un­ happy consequences. In particular, domestic Cho arcs are presently unique in that they are the only domestic arcs which are not unisponsored, as expressed in PN law 18, The Employed Local Successor Law. However, if we were to adopt the view that domestic Cho arcs are sponsored only by their prede­ cessors, we could not only generalize PN law 18 to eliminate the distinction between Cho arcs and nonCho arcs, we could combine the law in question with PN law 4, The Self-Sponsor Law, to achieve a single general princi­ ple expressing a limitation on the number of sponsors of all domestic arcs:

358

8. CHO ARCS

(131) Potential PN Law Domestic(A) -» Unisponsored(A) . From (131) would follow not only the current PN law 4, but also the result that all local successors have no sponsors distinct from their predecessors. On these grounds, it thus seems that a theory in which domestic Cho arcs have only predecessor sponsors is far more general and elegant than the current theory. Our most current view is thus that, contrary to the earlier development, domestic Cho arcs should not differ from other local successors, and should be unisponsored. However, a theory along these lines has not yet been fully worked out. Observe that some of the theorems in section 2, e.g., Theorems 60, 61, and 62, depend on the dual sponsorship of domestic Cho arcs. Thus, in abandoning this, we must find new proofs for these principles, which seem to us APG truths, or else we must stipulate them as PN laws. Ultimately, we are confident that a theory of APG with unisponsored domestic Cho arcs can be successfully stated. One basis for this is that in the present theory the nonpredecessor sponsor of a domestic Cho arc is uniquely picked out independently of the existence of the sponsor pair by the fact that it is the (necessarily unique) overrunner of the Cho arc pred­ ecessor. Hence, for talking about the relations between the Cho arc and the arc currently taken to be the "second sponsor," the sponsor pair is really redundant and unnecessary. However, practical limitations force us to leave a precise development of what we now take to be the maximally desirable theory of Cho arcs as a task for future work.

CHAPTER 9 FURTHER PRINCIPLES GOVERNING THE DISTRIBUTION OF CHO ARCS 9.1. The problem Chapter 8 did not deal with the problem of distinguishing between legal analyses like those in (8.30) and (8.31) and otherwise identical structures where UN and, e.g., Mary are interchanged. The legal struc­ tures are given in (1), and the corresponding illegal analyses in (2): a.

Joe

UN

(was) tickled

b, Cho

Mary (was) tickled Joe

Our assumption is that both (2a,b) and all similar structures must be ex­ cluded from the class of well-formed PNs. However, since the correspond­ ing structures of (1) and (2) differ only by the interchange of the nominals UN and Mary, none of the laws so far proposed exclude the forms of (2). For none of these laws distinguish different types of nominals heading arcs of identical types. What is involved, we suggest is two different

360

9. THE DISTRIBUTION OF CHO ARCS

(2) a.

Mary

Joe

b.

Cho/c.

UN

Joe

(was) tickled

groups of constraints, one relevant for blocking structures like (2a), the other for blocking those like (2b). We concentrate first on what is needed to block examples of the general form in (2a), where an arc headed by a nominal like Mary is, when overrun by a nonreplacer, erased by its overrunner rather than by a local successor.

9.2. Constraints on zeroing The solution is relatively simple although not very general. The class of nominals capable of occurring as the heads of arcs like A in (la) is extremely restricted. We currently know of at most two distinct nomi­ nal types whose occurrence in such cases is supported by reasonably clear examples, namely, the one we have been representing by UN and the one we earlier decided to call O . Assume then that there is some set of nonterminal nodes including those labeled with the grammatical category nodes UN and O but not containing the majority of nonterminal nodes,

9.2. CONSTRAINTS ON ZEROING

361

including those corresponding to nominals like Maty, the gorilla on the

corner, the proof that mice are immortal, etc. Call this set of nodes Inexplicit. We are claiming that the set of all nonterminal nodes is the union of Inexplicit and a disjoint set which is in fact its complement within the set of nonterminal nodes, Explicit. Formally: (3) a. Def. 147: a e Inexplicit «-> Node Label (a, UN) ν Node Label (a, 0). b. Def. 148: a e Explicit «-> a e NTNo A a / Inexplicit. With this equipment we can directly consider the problem of blocking structures like (2a). Assuming that nodes labeled UN and 0 are in Inexplicit and that no other nodes are, our claim is that all illegal struc­ tures like (2a) are such that the head of the illegally deleted arc is a mem­ ber of Explicit. Now, one cannot, of course, block all cases where a Nominal arc with an Explicit member as head is erased, since such era­ sure pairs are legion, e.g., the pair in (2a) itself, involving the B and C arcs. However, the illegal erase pair in (2a) involves erasure of a Nominal arc by an arc which is not only distinct but which does not overlap it. Thus, this erase pair is a zeroing pair in the sense of Chapter 5. The pair in question involves zeroing of a Nominal arc whose head is a member of Explicit. Legal assassinations of Nominal arcs headed by members of Explicit seem, however, to involve either unhooking, or zeroing by a re-

placer. In the latter case, the replacer is necessarily sponsored by the arc it zeroes. This suggests the possibility of imposing PN laws to restrict further the possibilities of zeroing, particularly of Nominal arcs headed by mem­ bers of Explicit: (4) PN Law 76 (The Nominal Arc Zeroing Law) Zeroes (Α, Β) Λ Nominal arc (B) Λ Not (Sponsor (Β, A)) -» Head(B) e Inexplicit. Given (4), only Nominal arcs headed by UN or 0 nodes can be zeroed by an arc they do not sponsor. The third conjunct in the antecedent exempts,

362

9. THE DISTRIBUTION OF CHO ARCS

inter alia, all replace structures 1 from the strictures of this law. Hence, The Nominal Arc Zeroing Law is perfectly compatible with the zeroing of a replacee by its replacer—hence compatible with the pair Zeroes(C, B) in (6), our analysis of (5): (5) John tickled himself.

John

himself

tickled

A number of other types of replacer structure have previously been con­ sidered, and further discussion of these is found in Chapters 11 and 13 in particular. All such structures are irrelevant to PN law 76, given the third conjunct in its antecedent. On the other hand, returning to the illegal erasure in (2a), under the assumption that the node represented by Mary is a member of Explicit, all such structures are correctly blocked by The Nominal Arc Zeroing Law. For under this assumption, the pair Zeroes(B, A) involves a violation of PN law 76, since B does not sponsor A. On the contrary, under the assumption that nodes like that represented by UN in (la) are not members of Explicit, (la) is correctly not blocked by The Nominal Arc Zeroing Law. PN law 76 then seems adequate to distinguish pairs of structures like (la) and (2a), given that the heads of the zeroed arcs can be (correctly) differ­ entially assigned to Inexplicit and Explicit respectively. Thismatteris discussed further at the end of this chapter. More precisely, although The Chomeur Law allows both (la) and (2a), given The Nominal Arc Zeroing Law, (2a) cannot be well formed. This

Another case involving a Nominal arc zeroed by a "clitic" arc which it foreign sponsors is considered in Chapter 12 in connection with linear order.

363

9.2. CONSTRAINTS ON ZEROING

new law thus serves to further restrict the kinds of structures which can exist in nonreplacer overrun situations. Further, if one finds a universal means of blocking structures like (2b) (see PN law 79 below), The Chomeur Law will entail that the pair Erase (B, A) in (la) is mandated. This follows since A is an overrun arc without either an employed or Cho arc local successor. Therefore, it must be erased by its overrunner, as indicated by The Overrun Erase Theorem of Chapter 8. Although PN law 76 has been motivated exclusively by contrasts like those in (1) and (2), this law correctly blocks a wide variety of other bizarre, and to our knowledge unattested, zeroing possibilities, a few of which are illustrated in (7): (7) a.

Joe

b.

Mary

Coit

Con

Joe

says

sings

sing Mary dance

c. 2

3

P

showed Mary Joe

364

9. THE DISTRIBUTION OF CHO ARCS

An erasure like that in (7a) would permit a sentence like: (8) *Joe says (that) sings. to exist and to mean "Joe says that Mary sings." An erasure like that in (7b) would permit a sentence like: (9) Joe sings and dances. to exist and to mean "Joe sings and Mary dances." An erasure like that in (9c) would permit a sentence like: (10) I showed Mary. to exist and to mean "I showed Mary to Joe." However, The Nominal Arc Zeroing Law blocks these and the infinite number of such other unknown structures. It is not surprising that there should be strict constraints on zeroing and, in particular, stricter constraints on this than on unhooking (see PN laws 77 and 78 below). For unhooking, unlike zeroing, can only lead to node deletion (see Definition 64 in Chapter 4) if there is more than one

erase pair linked in a "chain." Thus, while a single zeroing pair, Assassinate (Α, Β) , can lead to the deletion of the head of B , a single unhooking pair, Assassinate (C, D), cannot lead to the deletion of the head of D , since the head of D is also the head of C . Hence, unhook­ ing can lead to node deletion only in the case of sets of, e.g., the form: Assassinate (A, B); Assassinate (B, C); Assassin ate (C, A), where A, B, and C all overlap. In this case, if the head of A , B , C is not the head of any other arc, it is deleted. But Assassinate "chains" of this sort are unattested to our knowledge, and in Chapter 11 a law is proposed to exclude them from well-formed PNs (see PN law 93, The Assassination Independence Law). However, zeroing and self-erasure both can bring about node deletion with only a single erase pair (necessarily then not inconsistent with PN

9.2. CONSTRAINTS ON ZEROING

365

law 93). Given what is known of other generative systems, 2 it is not un­ reasonable to guess that zeroing and self-erasure are key determinants of the weak generative power of APG grammars. This is true under the assumption that a key factor determining this involves constraints on de­ letion. And given PN law 93, the possibilities for deletion are localized in zeroing and self-erasure. We anticipate, therefore, that many further restrictions ultimately should be placed on all types of zeroing and on self-erasure. An inadequacy of the account is visible at this point. While examples like those in (7) are correctly blocked by PN law 76, examples otherwise like (7) but with the nominal Mary replaced by, e.g., the nominal UN, are not. Yet these structures are evidently impossible as well. Thus, Eng­ lish has no sentence corresponding to such a substitution for (7a): (11) *Joe says that sings. = "Joe says that unspecified sings." It would seem that zeroing pairs allowed by PN law 76 for erased Nominal arcs whose heads are members of Inexplicit but not for those whose heads are members of Explicit are only possible in a restricted subset of the class of all cases, this class illustrated by (la). What class of cases is this? Evidently, that in which the erased Nominal arc is overrun by the nonreplacer arc which erases it. Further PN laws are necessary to guarantee this result. We propose two further laws, which, together with The Zeroing Out­ flank Law introduced with limited discussion in Chapter 8, yield the de­ sired results. The first restricts zeroing of a Nominal arc to a zeroer which is a neighbor if it is not sponsored by the erased arc: (12) PN Law 77 (The Local Zeroing Law) Zeroes (A,B) ANominal arc (B) ANot (Sponsor (B,A)) -> Neighbor (A,B) .

2

See such discussions as Putnam (1961), Peters (1973), and Peters and Ritchie (1973).

366

9. THE DISTRIBUTION OF CHO ARCS

Although we have inserted the second conjunct in the antecedent here for safety at this stage, we know of no cases where the result of eliminat­ ing this condition would be incorrect. All instances known to us of zero­ ing pairs in which the erased arc does not sponsor its assassin are local erasures. Thus, recall the erasure of the primary arc by the P arc local successor of a Nominal arc in the treatment of predicate nominal clauses in section 4 of Chapter 7. That erasure, mandated by PN law 40, is local erasure, and thus would fall under the more general version of (12) created by dropping the probably redundant second condition. Obviously, The Local Zeroing Law by itself suffices to block struc­ tures like those formed from (7a) and (7b) by replacing Mary by UN, since these are foreign zeroings in which the assassin is not sponsored by its victim. However, the result of the parallel substitution in the case of (7c) is not directly blocked by PN law 77, for this is a local erasure. Before considering how such cases can be eliminated, we should stress that the third, negative sponsor, condition in The Local Zeroing Law is based on our analysis of certain cases, those referred to in note 1, in which a graft can zero its foreign sponsor. One such case involving pronominal clitics is treated in (12.12). PN law 77 has, of course, no effect on structures where a replacer erases its replacee, since such erasures are local. Returning to cases like (7c), where an arc P-headed by Joe is zeroed by an arc P-headed by Mary, although these are not blocked directly by The Local Zeroing Law, all such cases are precluded by this in combina­ tion with The Zeroing Outflank Law of Chapter 8: (13) PN Law 65 (The Zeroing Outflank Law) Local Zeroes (Α, Β) Λ Nominal arc (B) -> Outflank (A, B) . For PN law 77 requires that such zeroings be local zeroings, which guar­ antees that the antecedent of The Zeroing Outflank Law is met. This then requires that the two arcs be related by Outflank. This means, inter alia, that they must have the same R-sign, a condition failed by the version of (7c) in question, which is hence blocked.

9.2. CONSTRAINTS ON ZEROING

367

The underlying assumption of PN law 65 is that in most cases local zeroing of a Nominal arc is done by a replacer, which is necessarily an outflanker. This law then establishes outflanking as a necessary concom­ itant of any such erasure. Ultimately, this will mean, via the next law to be stated, that if local zeroing of a Nominal arc does not involve replacing, it must involve the kind of overrunning found in, e.g., (la). Our informal claim above was that zeroing of Nominal arcs of the sort found in (2a) is only found in overrun situations, a stronger constraint than so far imposed, which limits the zeroing in question to same-sign Term arcs. We thus propose further that:

(14) PN Law 78 (The Outflank Overrun Law) Assassinate (Α, Β) λ Outflank (Α, Β) a Not (Replace(A, B)) -» Overrun (A, B) . This law precludes the possibility that, e.g., an Oblique arc or a Cho arc might be zeroed by an outflanker which is not a replacer. It limits this possibility to the single case of overrunning. Together, The Nominal Arc Zeroing Law, The Local Zeroing Law, The Zeroing Outflank Law, and The Outflank Overrun Law impose narrow conditions on possible Nominal arc zeroings, particularly in cases where the zeroed arc is not the sponsor of its assassin. Each of the last three laws, as it were, "feeds" the fol­ lowing law. The Local Zeroing Law requires that that the relevant zero­ ing be local. The Zeroing Outflank Law then requires that local zeroing of a Nominal arc involve outflanking. And finally, The Outflank Overrun Law requires that zeroing involving outflanking, but not replacing, be a case of an overrun arc erased by its overrunner.

9.3. A constraint on arcs headed by UN nodes Evidently, the laws proposed in this chapter so far have no bearing on the ill-formedness of (2b)-like structures. Our view is that what is in­ volved here is that an arc headed by an UN node cannot sponsor a Cho arc successor. We propose a principle, particular to the terminal node UN,

368

9. THE DISTRIBUTION OF CHO ARCS

which accounts for this, and which has other desirable consequences. First, let us refer to any node labeled with the grammatical category node UN as an UN node. Formally, an UN node is any node like 53 in: (15)

53 L α UN

Our basic idea is that, unlike the typical (nominal) nonterminal node, an UN node can never be the first node of more than one arc (we revise this slightly below to take account of the role of quantification). An ini­ tial inadequate statement of this principle would be: (16) Head Label (UN, A) A Head Label (UN, B) -» A = B . Thus (16) would block all R-graph fragments of the forms: (17) a.

55

IOO UN

b.

55 7!

100 UN

In (17a), the UN node 100 is the head of two neighboring (hence parallel) arcs, while in (17b) the UN node 100 is the head of two nonneighbor arcs. Both situations are precluded by (16).

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

369

One can immediately see that (2b) in particular is blocked by (16) and, more generally, that all similar structures are precluded. It follows direct­ ly from (16) that an UN node can never be the head of a (domestic) Cho arc (see Theorem 82 below). For such arcs necessarily have predecessors, and hence their heads must occur as heads of more than one arc. We saw in Chapter 8 that The Chomeur Law divided all cases of over­ running into two disjoint, exhaustive subsets. The first involves those situations where the overrun arc must sponsor a local successor, and has two subcases: (i) where the successor is a Cho arc; (ii) where the suc­ cessor is an employed arc. The second involves cases where the overrun arc is assassinated by its overrunner. Given (16) and The Chomeur Law, the only possibility for an overrun arc whose head is an UN node is to be assassinated by its overrunner (see Theorem 80 below). For the other possibilities, (i) and (ii) above, yield contradictions of (16). Hence, (16) explains the contrast between the well-formed (lb) and the ill-formed (2b). From this point of view alone, (16) deserves serious consideration. Moreover, such a principle, in combination with other APG assumptions, makes other restrictive claims about human sentences which seem correct. Consider first the claim made several times above that so-called "coreference" is correctly represented in terms of multiple, overlapping selfsponsoring arcs 3 (this idea is developed in Chapter 11). See the analysis of (5) in (6) above. This analysis combines with (16) to predict that UN nodes can never be involved in "coreference" (see Theorem 83 below). There is significant evidence for this view, including most of the data dis­ cussed in Grinder (1971). In particular, since we analyze short passives as involving an initial 1 arc with an UN node head, the well-known im­ possibility of pronominalization in such cases follows directly. For exam­ ple, (16) explains the contrast between Grinder's (1971: 186) examples like (18a,b) and (18c,d): q

More precisely, these must be structural arcs, and, in general, the type of structural arc whose head is normally a nominal, e.g., Nominal arcs, and a few other types.

370

9. THE DISTRIBUTION OF CHO ARCS

(18) a. Maxine was kissed by someone and he didn't even say whether he enjoyed it. b. Maxine was told by someone that she had to kiss him. c. Maxine was kissed and he didn't even say whether he enjoyed it. d. Maxine was told that she had to kiss him. In (18c,d) the italicized pronouns cannot be understood as "«(referential with" (in our terms, as heads of arcs sponsored by the arc with the rele­ vant head) the initial 1 of the passive clauses. In (18a,b), such "coreference" is possible, illustrating a contrast between, e.g., someone, which behaves like an ordinary nominal, and UN.4 Under the assumption that the nominal nodes corresponding to something, someone, etc., are members of Explicit, these contrasts follow from (16) since "understood coreference" in cases like (18c,d) would require the UN node to appear as head of at least two distinct arcs. A similar point holds for clauses with UN node-headed 2 arcs, like (19a), which contrasts with (19b): (19) a. Melvin ate. b. Melvin ate something. There is, as pointed out in Chapter 8, section 6, strong evidence, e.g., in Basque (see Postal [1977]),5 that clauses like (19a) involve an initial 2

^Although subtle, there is a semantic contrast between UN nodes and those corresponding to something, correlating with their syntactic contrasts. Something is more individuated than an UN nominal. Thus, imagine the following situation. An individual named John is simultaneously shot with a machine gun, electrocuted, and submerged in molten gold. Under these conditions, (i) seems anomalous but not (ii)·. (i) John was killed by something. (ii) John was killed. We have no proposal about how to represent the difference between something and UN nominals. It is, however, important for our discussion that something not be an UN nominal, since it manifests none of the grammatical properties we associate with the latter. ^Postal (1977) argues that the analogues of examples like (19a) must have initial 2 arcs, based on the facts of verb agreement, auxiliary choice, and case

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

371

arc. .We take the head of this to be an UN node. Such clauses may also, in English, involve antipassivization, as illustrated for French in (8.24), but this is not relevant here. However, one can then predict from (16) Grinder's(1971: 186) observations to the effect that: (20) a. Melvin ate something and it was green. b. Melvin ate and it was green. In (20a), the it can be "coreferential" with the nominal representing what was eaten, but not so in (20b). Other similar cases are discussed by Grinder. More generally, it follows from (16) that UN nodes can never participate in so-called "coreference." While (16) precludes "coreference" for UN nominals, it does not pre­ clude the possibility of two or more distinct UN nodes occurring in the same R-graph or even in the same clause. The latter possibility is illus­ trated in the following German example:6 (21) Es wurde gegessen. it became eaten. On one (irrelevant) reading, es here is an anaphoric pronoun, and the exam­ ple is roughly equivalent to an English clause like "it was eaten." How­ ever, (21) has another, impersonal structure, on which es is a dummy

marking. In all respects, such clauses are treated as transitive in Basque. Simi­ larly, Harris (1976, 1977) shows that in Georgian, initial ergative 1 arcs are treated specially with respect to case marking, determining the marker mier if, roughly, they have ultimate R-successors which are not Term arcs. However, as predicted from the transitive analysis of clauses like (19), the nominalizations of these in Georgian yield mier, consistent with the view that in the nominalizations the initial ergative 1 arc has a nonTerm arc successor. 6 An English example of the same sort is: (i) Melvin was written to. which has an UN node as head of its initial 1 and another as head of its initial 2. A French example is: (ii) Il Iui a ete repondu par trois fois. It to him/her has been answered by 3 times = "He/she was answered 3 times." which has an UN node as head of its initial 1 and another as head of its initial 2.

372

9. THE DISTRIBUTION OF CHO ARCS

nominal. On this reading, (21) means "unspecified ate unspecified," quite distinct from "unspecified ate itself." On the relevant reading, (21) simply says that (an) unspecified entity(ies) ate (an) unspecified entity(ies). We would represent just the initial arcs of this sentence as follows (we ignore noninitial arcs because they involve questions about dummy nominals only treated in detail in Chapter 10): (22)

τ

50" '60

UN

Both the 1 arc head, 50, and the 2 arc head, 60, of this structure are UN nodes. But, since neither occurs as the head of more than one arc, (16) is not violated and no "coreference" is understood. (22) illustrates the fact that the constraint in (16) in no way precludes the possibility of the terminal node UN occurring on more than one arc. As with arcs C and D , whose tails are respectively 50 and 60 in (22), however, all such arcs will, via The Termination Condition defining R-graphs (2.52g), be terminations. Hence, (16) refers to structural arcs whose heads are the tails of UN termi­ nations. It makes a claim about arcs like A and B in (22), not about terminations like C and D. Another important consequence of (16) is that clauses with UN nodeheaded 2 arcs will not be subject to ordinary 7 passivization: (23) a. Melvin ate something. b. Something was eaten by Melvin.

7 This word distinguishes passives like English (23b) from so-called reflexive passives. See the four-way distinction in Perlmutter and Postal (1977).

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

373

c. Melvin ate. d. *Was eaten by Melvin. (23d) is blocked by (16) because it would have the partial structure: (24)

IO C|C2

55 Melvin UN

(was) eaten

For, in (24), the UN node 55 is the head of both C and D. There may be, and probably are, other principles relevant at least for English which also block examples like (23d). In particular, one can probably specify for English that, informally: (25) The head of a final stratum 1 arc (required in each basic clause stratal family by PN law 44 (The Final 1 Arc Law)) cannot be an UN node. (25) seems necessary because, e.g., (16) would not block, but (25) would, cases like: (26) a. *Sang = "Unspecified sang," b. * Kissed Betty = "Unspecified kissed Betty." c. * Talked to the cops = "Unspecified talked to the cops." In none of these structures is there any reason to postulate that any nomi­ nal node occurs as head of more than one arc. But, although (16) is not relevant, the examples are all bad. However, (16) is intended to be the essence of a PN law and thus relevant not only for English but all lan­ guages. In some of these, examples parallel to (26) may be well formed.

374

9. THE DISTRIBUTION OF CHO ARCS

(16) would claim that, even in such languages, the analogue to (23d) would be ill-formed. We have not been able to test this claim, but it shows that, in the domain of passivization, (16) is not necessarily rendered re­ dundant by principles like (25). Further, consider examples like: (27) a. There exist gorillas. b. There arose a new theory. Suppose, adopting a basic stage 2 RG insight, we take these clauses to involve initial 2 arcs. That is, assume these are among those clauses discussed in Chapter 7 as involving initial unaccusative arcs. Suppose they also involve a ghost arc (see the definition in (10.3) in Chapter 10) with there as head whose R-sign is 1. Then a partial structure for (27a) in APG terms would be: (28)

there gori lias Under these assumptions, the head of the initial 2 arc corresponding to

gorillas occurs as head of more than one arc in such cases, since the 2 arc in question meets the antecedent conditions of PN law 46, The Unac­ cusative Law, and must thus have a 1 arc local successor. (16) therefore predicts that substitution of an UN node for gorillas cannot yield wellformed structures: (29) a. *There exist(s). b. *There arose.

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

375

However, the explanation of the ill-formedness of examples like (29) via principle (16) depends on assumptions we have not justified and which we are not now in a position to justify completely. Examples like (29) support a principle like (16) only under the assumption that (28) is the only viable APG structure for (27a). However, there are many other possi­ bilities. To clarify the issues, it is worth considering a few of these, the discussion being in effect an introduction to problems dealt with further in Chapter 10, devoted to dummy nominals. Alternative structures for examples like (27) depend on whether the entrant arc headed by there is taken to be a 1 arc or a 2 arc, on whether the initial Nuclear Term arc (required by PN law 43) is taken to be a 1 arc or a 2 arc, and on which arc sponsors the dummy nominal-headed entrant arc. One analysis is that in (28), which we believe to be at least partly correct because we accept the initial unaccusative hypothesis in general and because we believe in particular that verbs meaning "exist" always fall under the range of this hypothesis. A second analysis would be the following, in which the initial Nuclear Term arc is also an unaccusative arc, as in (28), but where this has a Cho arc local successor determined by a 2 arc entrant headed by there, yielding:

there exist

Both (30) and (28) are consistent with the initial unaccusative structure for verbs like "exist." Moreover, although it is ultimately important to decide between these two (on the assumption that one is correct), this is not strongly relevant here. For even if (30) is correct, the support for principle (16) from examples like (29) remains. The "correspondent" of

376

9. THE DISTRIBUTION OF CHO ARCS

(30) for the case where the initial Nuclear Term arc is headed by an UN node would be:

there

exist

UN

And (31) is not ruled out by any previous considerations independent of (16). In particular, (31) is consistent with The Unaccusative Instability Law of Chapter 7, since C is not unaccusative at C2 . A third possible analysis of examples like (27) would take the initial Nuclear Term arc to be a 1 arc (violating the unaccusative hypothesis as linked to "exist") and the entrant arc headed by there also to be a 1 arc, yielding:

Cho\c·

there

gorillas

exist

Except for the claimed linkage between initial unaccusatives and verbs meaning "exist," which we have not formalized, (32) violates no con­ straints on PNs we have proposed. However, if (32) is correct, facts like (29) are explained without principle (16), since the structure for (29a) based on the assumptions underlying (32) would be:

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

there

UN

377

exist

For, as discussed in the next chapter, structures like (33) violate basic requirements on certain types of entrant arcs headed by dummy nominals. Such arcs must sponsor domestic Cho arcs (see PN law 85, The Stable Ghost Arc Sponsor Law in Chapter 10). But A in (33) sponsors no arc at all. A fourth analysis would take the initial Nuclear Term arc of the basic clauses of cases like (27) to be an unaccusative arc, with the entrant arc headed by there a 1 arc, yielding: (34)

P C|C2 there

gorillas

exist

However, (34) involves the same difficulty as (33), since A does not sponsor a Cho arc. Moreover, (34) violates an even deeper principle about the entrant arcs headed by dummy nominals, that referred to as The Ghost Arc Law in Chapter 10. (34) thus can be eliminated as a structure for (27a), under the assumptions about dummy nominals of Chapter 10.

378

9. THE DISTRIBUTION OF CHO ARCS

A fifth analysis would be the following, in which gorillas is head of an initial 1 arc and there the head of an entrant 2 arc: (35)

goril las

there

exist

However, as discussed in several places above and below, (35) is a pas­ sive structure, 8 and, given the independently existing rules of English,

would yield not the actual (27a), but the nonexistent: (36) *There is existed by gorillas. Hence (35) cannot be the structure of (27a). A sixth analysis would be for the initial Nuclear Term arc to be a 2 arc and for the entrant arc headed by there to also be a 2 arc, as in (35), yielding: (37)

Cho

gorillas

g

P C|C2C3

there

exist

See the discussion in Chapter 8, particularly the representation in (8.59). That is, (35) is a structure in which an arc accusative at c^ has a 1 arc local successor whose first coordinate is c J c ^ ·

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

379

But," like (35), (37) is a passive structure and would also yield (36) in­ stead of (27a). Moreover, (37) violates the stage 2 RG principle referred to as The Advancee Tenure Law. And while we cannot attempt to develop this principle in detail here, it has a great deal of support.9 Thus, on various grounds, (37) cannot be the structure of (27a). It follows that there are, given so far formalized APG principles, at least three apparently viable analyses for examples like (27a), namely, (28), (30), and (32). The former two are both initial unaccusative struc­ tures, and either one provides support for a principle like (16). The latter is not an unaccusative structure and, if it is correct, no support for (16) is forthcoming. Our claim is that (32) is ultimately eliminated as a possible PN by the requirement that "exist" head an arc which is a neighbor of an initial unaccusative arc.10 If so, then one can indeed extract support for (16) from facts like (29). But this support depends on the evidence for

Q

The claims involved in The Advancee Tenure Law can be "translated" into APG terms (with the usual caveats) as: (i) Local Successor (Α, Β) A Local Successor(C j D) Λ Term arc (AvC) -» Not(D-Facsimile(A, C)) . We know of no problems with (i) where the arc instantiating the variable A is a 1 arc. However, the law seems falsified when A is a 2 arc in languages like Kinyarwanda (see Gary and Keenan [l977], Perlmutter and Postal [to appear b]) where there are apparently multiple "advancements" of Oblique nominals to 2hood. Hence a viable PN law version of (i) will apparently have to replace the third con­ junct of the antecedent of (i) by the less general: (ii) 1 arc (A AC). 10 The claimed contrast between intransitive predicates taking initial unaccusatives and those taking initial unergatives shows up in an extremely interesting way which interacts with and supports The Advancee Tenure Law as well as the unaccusative hypothesis. It is claimed that the following predicates divide up as indicated: (i) a. Co-occur with initial unaccusative arcs exist, drip, sink, rise b. Co-occur with initial unergative arcs dream, meditate, smile, swim The Advancee Tenure Law then determines that verbs like those in (i,a) cannot be the predicates of passive clauses. For this would require not only that the Unaccusative arc have a 1 arc local successor, but that some other distinct neighboring arc have a 1 arc local successor, the two 1 arc local successors then being facsimiles in violation of (i) of note 9. The relevant passive structures would have the form:

380

9. THE DISTRIBUTION OF CHO ARCS

giving "exist" clauses initial unaccusative representations, and this is a complex matter, not yet formalized as an aspect of APG theory. A further implication of (16) as it interacts with the unaccusative hypothesis should be mentioned, although we have not been able to test it.

(ii)

C|C2C3

Cho

Here C is the initial unaccusative arc, B its 1 arc successor required by The Unaccusative Law, A the Cho arc successor of the latter, motivated by the over­ running 1 arc, D. (ii) violates The Advancee Tenure Law because two local suc­ cessors, B and D, are distinct 1 arc facsimiles. On the contrary, for otherwise parallel initial unergative structures, the 1 arc successor due to passivization is a facsimile of a distinct 1 arc. But since the latter 1 arc is an initial 1 arc, hence not a local successor, no violation of The Advancee Tenure Law ensues. That is, (ii) would not violate this law if B was a self-sponsoring arc and C did not exist. Significantly, among English nominals there is a subset of nominalizations of predicates like those in (i,b) which manifest passive form, as indicated by the prepositional phrase with by. But there are no such nominalizations of intransi­ tive predicates like those in (i,a): (iii) a. the existence

(of il*t fby

demons

b. (the) dripping of the faucet *by of (the) sinking the ship *by /of (in) I the price of steak d. (the) rise l*by J (iv)

dreaming by children meditation by experienced monks smiling by moviestars swimming by individuals with heart trouble

We take this to indicate that the nominals with by involve nominalized clauses which are impersonal passives (see further discussion of these in Chapter 10). This is not possible for reasons illustrated in (ii) with predicates taking initial unaccusatives, given The Advancee Tenure Law. The deeper claim is that con­ trasts like those briefly illustrated in (i) are systematic cross-linguistically. That is, the same (semantically) intransitive predicates will take initial unaccu­ satives or unergatives in all languages.

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

381

We observed that English seems to have a constraint like (25), which blocks all clauses whose final stratum 1 arc is headed by an UN node. Suppose, within our system of assumptions, that English had no such con­ straint. Examples like (26) would then, mutatis mutandis, be well formed. However, given the unaccusative hypothesis, and, in particular, the claim (which we make) that the self-sponsoring Nuclear Term arcs of a basic clause are determined by the logical node labeling the primary of the clause, we would still predict that verbs (like "exist") requiring initial unaccusative arcs would be ill-formed in contexts like (2 6). That is, even without (25), we would predict: (38) *Exists = "Unspecified exists" since this would have to have under the unaccusative 2 hypothesis, the structure in (39), which violates (16).

UN

exists

The analogous distinction between unaccusative and other predicates is, we suggest, the explanation, via The Advancee Tenure Law, of such contrasts as that between: (v) a. The gorilla sat on the table. b. The statue sat on the table. (vi) a. The table was sat on by the gorilla. b. *The table was sat on by the statue. In (v) there are distinct, homonymous verbs, That in (v,a) is a transitive, probably the causative of that in (v,b), with the expected reflexive pronoun surface object not present (The gorilla sat himself on the table is grammatical for some people in some contexts). The predicate in (v,a) being transitive, the gorilla in (v,a) is the head of an initial ergative arc, and hence (via) is not blocked by The Advancee Tenure Law. But (vi,b) is, since the statue corresponds to an initial unaccusa­ tive arc head. Considerations like these give an initial hint of the interest and predictive power of both the unaccusative hypothesis and The Advancee Tenure Law.

382

9. THE DISTRIBUTION OF CHO ARCS

Thus, evidence bearing on the unaccusative hypothesis, which is central to any claim that facts like (29) support a principle like (16), is in princi­ ple derivable from languages not having an analogue of (25). For these, we predict, on the basis of semantic determination of initial unaccusative versus initial unergative structures, contrasts like: (40) *Exists = "Unspecified exists" (41) Sings = "Unspecified sings" In any event, it seems that (16) is a hypothesis which, at this stage, deserves inclusion in the set of proposed PN laws. For, together with PN law 76, The Nominal Arc Zeroing Law, it, inter alia, correctly divides up the cases of overrunning not involving replacers, divides them up as they are divided in, e.g., (1) and (2). However, before (16) can be stated pre­ cisely as a PN law, it is necessary to deal with a further aspect of UN nodes. From a logical point of view, it seems to us that an UN node is a node which is (i) bound by an existential quantifier, and (ii) not "characterized.' By the latter we mean that it is not involved, beyond the minimum,11 in, e.g., restrictive relative clauses, etc., which serve to restrict the refer­ ence of other nominal nodes. Now, while we have no fully developed con­ ception of the representation of quantifiers in PN terms, certain general properties of such a description seem clear. Quantifiers will have to stand in "higher" parts of L-graphs than the nodes corresponding to the variables they bind, as in any system of logi­ cal representation known to us. And since, if present in S-graphs, they do not in general stand in such positions in S-graphs, arcs of which quantifier nodes are heads will have to occur as successors arc command­ ed by their precedecessors. Let us represent the node corresponding to

11 This vague and unclear notion is illustrated by the RR arc in (42) below, which represents the minimum presence of a restrictive relative clause with UN structures.

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

383

the existential quantifier as 3, and let us assume that occurrences of 3. P-head P arcs of clauses, just as ordinary predicates like KISS, KNOW, etc. Then, a partial representation of a clause like (23c) which makes the quantifier structure more explicit might be: (42)

IO

L

There is unquestionably a certain degree of arbitrariness in (42), although it does not seem unnatural to us to represent the restricting phrase of a quantifier as a restrictive relative. 12 In any event, one element of (42) seems inevitable under any concep­ tion of UN nodes as bound by existential quantifiers. Namely, the UN node, the node bound by the quantifier, 55 in (42), must occur as the head of more than one arc. In (42), 55 occurs as the head of both A and D , the former indicating its role in the quantificational structure proper, the latter its role in the restricting expression which yields the S-graph clause. Principle (16) above is incompatible with structures like (42). Rather than taking this to show either that the principle represented by (16) is wrong or that (42) is a wrong structure (in the crucial respects), we take this conflict to indicate only that the principle we intended (16) to repre­ sent is slightly more complicated, and hence (16) is not an adequate formu­ lation of it. 12

As indicated in the text of Chapter 4, section 2, Hie L-Graph No Circuit Condition precludes the possibility that C in (42) could be a self-sponsoring arc.

384

9. THE DISTRIBUTION OF CHO ARCS

Since all UN nodes are assumed to be bound by existential quantifiers, every such node must occur as head of an arc whose tail is also the tail of an arc labeled Ή (the node 10 in (42)). The correct formulation of the principle so far represented as (16) must then minimally exclude such arcs, arcs like A in (42). To make this more precise, the following definition picks out the relevant class of arcs for exclusion from the scope of the principle in question: (43) Def. 149: Binder Arc(A) *-» (3B)(Colimbs(A j B)ASelf-Sponsor(AAB) λ P arc (B) Head label (Ή,Β) AStructural(A)) .

(43) specifies as a binder arc any arc which is a distinct self-sponsoring neighbor of the primary arc support of a Ή termination. As stated, this definition limits binder arcs to existential cases. A fuller treatment of quantification in such terms would obviously expand the last conjunct in the defining expression to include, in addition to 3 , the other logical nodes representing quantifiers distinct from the existential quantifier. A in (42) is then a binder arc. With this equipment, the principle so far represented as (16) is statable in such a way that it has all the conse­ quences attributed to (16) and yet is not incompatible with the inevitable features of (42): (44) PN Law 79 (The UN Node-Headed Arc Limitation Law) Head label (UN ,A) AOverlap(A j B) ANot (Binder Arc(AvB)) -> A = B . PN law 79 allows an UN node to head more than one arc just in case the additional arc is a binder arc, as in (42). If we assume, as seems in­ dependently necessary, that no node can be the head of more than one binder arc, 13 (44) allows UN nodes to head two arcs. If we assume, as also seems necessary, that every UN node is the head of a binder arc, then it will turn out that every UN node is the head of exactly two arcs,

more standard terminology, no variable can be bound by more than one quantifier.

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

385

one a binder arc, one not. Under these conditions, the original conse­ quences of (16) now follow from PN law 79, as desired. It is worth showing this a little more precisely. We therefore list sev­ eral theorems, showing that overrun arcs headed by UN nodes must be erased by their overrunners, that such arcs cannot have successors, and hence no Cho arc successors, and, finally, that D-overlapping, selfsponsoring UN node-headed nonbinder arcs are impossible. (45) THEOREM 80 (The UN Node-Headed Arc Erase Theorem)

Overrun (A, B ) Λ Head Label (UN,B ) Λ Not {Binder Arc(B)) -» Erase(A l B). Proof. Assume Overrun (A', B') and Not (Binder Arc (B')) and that the head of B' is labeled UN. Assume the contrary of the theorem, hence: (i)

Not (Erase (A', B')).

It follows from The Overrun Erase Theorem that: (ii) (3C) (Local Successor (C, B')). Suppose C' is the successor of B'. Therefore: (iii) Overlap (C', B'). Now, since C' is a successor and hence not self-sponsoring, it is not a binder arc. Hence, C' and B' are overlapping UN node-headed nonbinder arcs, contradicting The UN Node-Headed Arc Limitation Law. QED. It is Theorem 80 which directly shows that, e.g., B must erase A in structures like (la). Thus APG theory universally determines such erasures. Ultimately, we would like to prove a stronger theorem than (45), in which the third conjunct in the antecedent was unnecessary. But to do this, we need to

study

the properties of "quantificational" clauses, that

is, those containing binder arcs, a topic we must leave for future research. Next, consider UN node-headed arc successors: (46) THEOREM 81 (The UN Node-Headed Arc Successor Theorem)

Head LabeKJJN,Α) λ Not(Binder Arc(A)) -+ /Voi((3B) (Successor (B, A)). Proof. Assume that A' is head labeled UN and is not a binder arc. And

386

9. THE DISTRIBUTION OF CHO ARCS

assume, contrary to the theorem, that there is a B' such that; (i) Successor (B', A'). Since B' is a successor, it cannot be self-sponsoring and hence not a binder arc. But B' and A' overlap. Therefore, since A' is head labeled UN, The UN Node-Headed Arc Limitation Law requires that A' = B', which contradicts (i), given the irreflexivity of the successor relation. QED. As in the case of (45), we would ultimately like to prove a stronger theorem than (46), in which the second conjunct of the antecedent is eliminated. The same comments made about (45) in this regard hold. It then follows from (46) that: (47) THEOREM 82 (The UN Node-Headed Arc Cho Arc Successor Theorem) Head LabeKJJN,A) a Not(Binder Arc(A)) -> Not((3B)Successor(B,A) a Cho arc(B)) . Proof. Immediate from Theorem 81. QED. Finally, we show that UN node-headed arcs cannot "participate in coreference," by which we mean that there cannot be two self-sponsoring UN node-headed arcs which are not binder arcs: (48) THEOREM 83 (The Overlapping Self-Sponsoring UN Node-Headed Arc Theorem) Self-Sponsor (Α αΒ) λ Over/ap(A,B) λ Head Labef(UN t A) λ Not(Binder Arc(AvB)) -» A = B , Proof. Immediate from PN law 79. QED. Theorems 80-83 reveal that PN law 79 imposes strict constraints on UN node-headed nonbinder arcs, yielding as formal implications those conse­ quences earlier seen to follow from (16) and necessary to explain the rele­ vant empirical facts. These theorems make unnecessary any languageparticular rules to account for, e.g., the existence of the pair Erase (B, A) in (la), the impossibility of (2b), and the facts in (18), (20), and (23).

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

387

Together, The UN Node-Headed Arc Limitation Law and The Nominal Arc Zeroing Law essentially complete the job of dividing up the cases in (1) and (2). Where The Chomeur Law and previous conditions allow all four structures as viable PNs, The Nominal Zeroing Law eliminates (2a) and The UN Node-Headed Arc Limitation Law eliminates (2b). Moreover, since none of these structures contain employed local successors for the overrun arcs, The Chomeur Law determines that B must erase A in (la) and that A must have a Cho arc successor (and hence eraser) in (lb). Thus, those features which distinguish (la, b), but which are not accounted for by The Chomeur Law, are now consequences, and require no languageparticular statements. Hence, even though we treat, e.g., short passives as partially different from long passives, we do so in ways determined in­ ternal to APG linguistic theory. There are many additional properties of, and mysteries about, UN nodes which deserve study. However, we can specify here only one further aspect of the unique element UN. In no example analyzed with an UN node has that node been the tail of a sar/ace arc which R-governs a phono­ logical node. More loosely, nominals represented by UN nodes never have had any phonological realization. We suggest it is a universal property of such nominals that they cannot have phonological consequences.14 We must then guarantee this result. It will have been observed that in some cases, e.g., those like (la), the arc headed by an UN node is erased by a distinct arc, i.e., zeroed. This, together with an independently need­ ed PN law (see PN law 81 below), guarantees the nonoccurrence of phono­ logical representations of UN nodes. However, in other cases, like (23c), no zeroing pair is present. One must thus account for the erasure of the relevant arcs in such cases. That is, one must account for the erasure of the initial 2 arc in examples like:

14 This is noted in Postal (1977), where the ad hoc device of labeling with a special grammatical node, Silent, was proposed. But the basic assumptions of APG, in particular, the Erase relation, render constructs like Silent unnecessary.

388

9. THE DISTRIBUTION OF CHO ARCS

(49) Melvin ate. which evidently involve no S-graph 2 arc. To accomplish this, we pro­ pose the following PN law particular to UN node cases: (50) PN Law 80 (The UN Node-Headed Arc Self-Erase Law) Head label(UN,A)

Λ

Not ((3B)(Assassinate (B,A))) -> Self-Erase(A).

This law now forces cases like (49) to involve self-erasure of the initial 2 arc, as in (51) (ignoring, inter alia, the superordinate elements relevant to quantification): 100

(51)

(!)

Melvin

More generally, PN law 80 guarantees that no arc headed by an UN node can be a surface arc. 15 However, structures like (51) raise an important problem. For, as things stand, (51) does not define an S-graph and is thus not a PN. The problem is that B in (51) is the only support of D , and B is erased but D is not. It follows that the surface arc set of (51) would not be

^As indicated by Theorem 45 in Chapter 6, all self-erasing arcs are final arcs. Hence, arcs like B in (51) are final arcs. This status is not in the slight­ est affected by the deletion of the head of the arc. This yields the right conse­ quences in cases like Basque, discussed in note 5, where arcs analogous to B are treated as final stratum arcs by rules of agreement and case marking. Such clauses are treated for these purposes exactly like those with visible direct objects, a consequence if, as we assume, the rules refer to final stratum arcs.

9.3. CONSTRAINT ON ARCS HEADED BY UN NODES

389

connected. This problem is not peculiar to situations with UN. It neces­ sarily arises in a wide variety of cases in which all the supports of some branch are erased. The generalization seems to be this. If A is a nonassassinated branch in the R-graph, Q , of some PN, but has no support arc in Q which is also in the S-graph of Q , then, where A is not tail labeled Cl, A must self-erase. We return to the final italicized restric­ tion below. Let us refer to an arc like A in such situations as an overmined arc. We will also sometimes be interested in the "opposite" situation, where supports lose all their branches: (52) a. Def. 150: Overmined(Arc) (A) *-* (ΉΒ) (Branch (A,B)) ANot ((3C) (Branch (A,C) ASurface Arc (C))). b. Def. 151: Undermined(Arc)(A) «-» (3B)(Branch(B,A)) ANot ((3C) (Branch (C,Α) λ Surface Arc (C))). Thus, an overmined arc is a branch which has no surface support, while an undermined arc is a support which has no surface branch. In terms of (52a), it is possible to force arcs like D in (51) to selferase, preserving the required connectedness of S-graphs: (53) PN Law 81 (The Overmined Arc Self-Erase Law) Overmined (A)ANot (Tail label (Cl,A)) ANot ((3B) (Assassinate (B,A))) -» Self-Erase (A). The Overmined Arc Self-Erase Law guarantees that an arc, A , whose tail is not a Cl node, self-erases whenever all of A's supports are in the range of Erase but A has no assassin. Given PN law 81, D in (51) necessarily self-erases, and the appropri­ ate S-graph for PNs like (51) is obtainable. This law will be relevant, inter alia, for most typical cases of self-erasure (not induced by PN law 81 itself), e.g., self-erasure of "pronominal" arcs like that illustrated in, e.g., (3.11). For, in general, such arcs will have branches. These branches will not otherwise be erased, will lack surface supports, and thus will be overmined. Moreover, they do not, obviously, have Cl node tails.

390

9. THE DISTRIBUTION OF CHO ARCS

We have not motivated the condition in (53) which exempts arcs with Cl node tails from its provisions. The rationale for this condition is our view that, e.g., there are R-graph branches with Cl tails without S-graph supports. In fact, given the structure proposed in (42), this is the case for A, B, and C in (51) itself. For the correspondents of these are all branches in (42), but none of the supports will be surface arcs. (42) is, we suggest, only a special case of a group of situations of this sort, that is, where a set of support arcs representing a superordinate quantifier structure do not occur as surface arcs but where (some of) their branches do. PN law 81 claims this is possible only if the heads of the "stranded" branches are Cl nodes, as is the case with node 100 in (51) (although we have not made explicit the L arc whose head is Cl). We can say some of this in a more familiar but less precise way. It means that "lowering" is possible only when the "highest" node into which another node is "lowered" is a Cl node. 9.4. Remarks on 0 nodes The view that UN nominals are always invisible is not inconsistent with the existence of nominals like French on, German man, etc. For our claim is that such nominals represent, not UN, but rather the other subject of Inexplicit, O nodes. Semantically, the distinctness of these two is manifested in the greater restrictiveness of on, man, etc. Where UN nomi­ nals can refer to any object(s) whatever, O nominals are restricted to reference to mind-possessing entities. These are usually called "human," as in the following discussion of Spanish from Aissen and Perlmutter (1976:9-10): We therefore call this construction by the traditional name of re­ flexive passive.

(27) Las propiedades se vendieron ayer. "The pieces of property were sold yesterday." (28) Estas canciones se cantan siempre primero. "These songs are always sung first." (29) Esta construccion se emplea con toda clase de sujetos. "This construction is used with all kinds of subjects."

391

9.4. REMARKS ON O NODES

The initial 1 of the construction illustrated by (27-29) is understood to be human. It never appears in surface structure in Spanish. We will refer to it as PRO. It is probably the entity that is realized as on in French and man in German. While we agree with the insightful identification of the initial 1 of cases like their (27)-(29) and on and man,16 the terminology "human" may be un­ fortunate. We suspect that 0 can be used to refer to Martians, personified steam engines, devils, angels, etc. Syntactically, O is distinct from UN in not being subject to PN law 79. This manifests itself in several ways. Restricting attention to French, we find the following indications that on can manifest "coreference":

(54) a. (Quand) on veut aller When

au marche, (on prend Ie bus).

0 wants to go to the market

0 takes the bus =

"When unspecified (mind-possessing being(s) = 0) want to go to the market, go shopping, 0 takes the bus." b. On ne se critique pas beaucoup, a MIT, cette annee. 0

self criticize not much

at MIT

this

year =

"0 don't criticize themselves much at MIT this year." In (54a), 0 is understood both as the 1 of the veut clause and the 1 of the subordinate aller clause; in (54b) 0 is understood both as the initial 1 and 2 of the clause. Secondly, unlike UN, 0 nominals can be the heads of 2 arcs which passivize, that is, which have 1 arc local successors: (55) On

a

ete

0 has been

beaucoup critique par ces gens. much

criticized by those people =

"0 was criticized a lot by those people." Such facts motivate the distinction made here between UN and 0 . None of this implies that 0 nominals are not themselves subject to constraints stricter than those on ordinary nominals, some of these

*®This dates at least to Perlmutter (1968: 29).

392

9. THE DISTRIBUTION OF CHO ARCS

possibly universal. For example, we know of no cases where an O node need be regarded as the head of a Cho arc. There are, in particular, no French passive clauses like (56b): (56) a. On a beaucoup critique pa. O has

much

criticized that = "0 criticized that a lot."

b. *£a a ete beaucoup critique par on. has been

by

O

Moreover, there is a French construction in which a dummy nominal (see Chapter 10) appears as 1, with the earlier stratum 1 appearing as a chomeur. (57) shows that this is not possible when the earlier 1 is an O nominal: (57) a. Trois enfants sont arrives hier 3

children

soir.

are arrived yesterday evening =

"Three children arrived yesterday evening." b. Il est arrive trois enfants hier soir. it

is arrived

"Three children arrived yesterday evening." c. (Quand) on est arrive aussi vite ... when

O

so quickly

d. *(Quand) il est arrive on17 aussi vite ... 17 Examples like (57d) might be blocked by a restriction more general than a claim that O nodes cannot head Cho arcs. Thus, there might be a condition valid for French requiring that O nodes only head 1 arcs. Passives like (55) would show such a constraint cannot hold at all strata, and would have to be limited to, e.g., final stratum arcs or perhaps surface arcs. However, examples like: (i) Ca finit par fatiguer (tiring O \ that finishes by to fatigue = "That ends up ·{ >' (becoming tiresome to Of indicate that such a constraint cannot refer to final stratum arcs, (i) seems to have, in its fatiguer clause, a self-erased 2 arc headed by an O node. But all self-erased arcs are final stratum arcs. Hence O nodes can head final stratum arcs in French. This leaves the possibility of claiming. (ii) A surface arc headed by an O node must (in French) be a 1 arc. TTiis would explain not only the failure of any surface Cho arc to be headed by an O node, but also the failure of surface 2 arcs, 3 arcs, etc., to have this property.

9.4. REMARKS ON O NODES

393

It seems then that there is a constraint of the form: (58) HeadLabel(OjA) -» Employed (A). Arcs headed by O nodes cannot be Cho arcs. At worst, (58) would be an unpredictable feature of the grammar of French and certain other languages. At best, it could be a PN law. Under the latter, a priori more desirable assumption, the claim would be that, e.g., the fact that (56a) has no pas­ sive "correspondent" and that (57d) is ill-formed are not ad hoc features of French but theorems of a principle which precludes O nominal chomeurs. As noted earlier, we regard nodes labeled O as the other so far justi­ fied members of the set Inexplicit. This allows O node-headed arcs to be erased by overrunning arcs, just as UN node-headed arcs. Our motivations for this arise from analyses like that suggested by Aissen and Perlmutter in the quotations above. If they are right, their example (27) would have, in our terms, the following partial analysis:18 However, (ii) is doubtful. For the surface constraint in question holds not really for O node-headed arcs, but for arcs whose heads determine the clitic on. In many cases, such arcs have heads which are not O nodes but which are nodes which otherwise yield, e.g., nous "we." It seems, therefore, that the French constraint limiting O nodes to surface 1 arcs is ultimately connected to the necessity for O nodes to yield the clitic on, only possible when those nodes head 1 arcs. In fact, if, as we suspect, on is not a nominal at all, but a verbal clitic, it would follow that no O node-headed arcs in French are surface arcs, and that the constraint is that the clitic on can only be determined by a final stratum 1 arc (of a "tensed" clause). It is thus not obvious to what extent a particular principle excluding O node-headed Cho arcs is rendered superfluous by a more general condition in French. It might not be an accident that although there are examples like (i) with erased final stratum O node-headed arcs, there seem not to be equivalents for final stratum Cho arcs. In particular, there is no "correspondent" of (57d) of the form: (iii) Il est arrive = "O arrived." (iii) can only mean "he/it arrived." But (iii) with the impossible O reading would not violate any constraints on surface arcs headed by O nodes or any constraints on the clitic on. If then the absence of forms like (iii) is not accidental, this supports a principle peculiar to Cho arcs headed by O nodes.

18

E l l a s here is a copy pronoun determining that the construction involved is a reflexive passive. The arc headed by ellas sponsors the arc in the verb headed by se, the latter arc zeroing its sponsor, but not violating The Nominal Arc Zero­ ing Law. See Chapter 11, section 8.

394

9. THE DISTRIBUTION OF CHO ARCS

(59)

las propriedodes

ellos

ayer

(se) vendieron

Here an arc headed by an O node is erased by an overrunning arc, just as previous examples of UN arcs. Postulation of structures like (59), more generally, the claim that both UN headed arcs and O headed arcs can be zeroed by nonreplacer overrunners raises the possibility that many constructions would be ambiguously analyzable with invisible O or invisible UN. Thus, we have offered no

principles which would prevent interchanging O for UN and conversely in all of the examples from various languages that have been cited. There are several possibilities. Either certain constructions are ambiguously analyzable with O or UN, or not. If they are, there is no problem, for the treatment so far permits both analyses. If certain constructions are not ambiguous, then a possible difficulty arises. Let us concentrate on Aissen and Perlmutter's example (27), repre­ sented in our terms in (59). If they are correct, a structure with O replaced by UN would be incorrect. Nothing we have said accounts for this. How­ ever, Spanish must have a rule limiting the class of reflexive passive con­ structions. The restriction that only O is a possible initial 1 in such constructions can be built into the relevant Spanish rule. Just so, if there are constructions which are incompatible with O and allow only UN, this can be built into the rules for the constructions in question. Recall that one of the two problems to which this chapter is addressed is to explain why structures like (2b) cannot exist. We wanted to account for the assumed fact that UN nodes cannot head Cho arcs. More generally,

395

9.4. REMARKS ON O NODES

it is necessary to explain why, when an arc headed by an UN node is over­ run by a nonreplacer, that arc cannot have a successor but must be erased by its overrunner. Our proferred explanation of this is PN law 79, The UN Node-Headed Arc Limitation Law. Since this law does not apply to nomi­ nal nodes labeled O , we do not predict that structures analogous to (2b) are ill-formed when the overrun nominal is headed by an O node rather than an UN node. We have not universally blocked any structures of, e.g., the forms: (60) a.

C ho,

Mary

(was) tickled

b

Mary

tickled

(60a) is a potential passive structure, while (60b) is. a potential antipassive structure (compare the analysis of the French clause in (8.24)). The fact that structures like (60a, b) are not so far excluded in princi­ ple is possibly a theoretical weakness since those considerations not directly linked to PN law 79 which suggest that (2b)-like structures do not exist also suggest that those like (60a, b) do not. However, we do not see any fundamental problem here. There are two logical possibilities: (i) PNs like (60a, b) may indeed exist, in which case the present system cannot be

396

9. THE DISTRIBUTION OF CHO ARCS

faulted for not blocking them; (ii), more likely, PNs like (60a, b) are im­ possible. There are, however, then possible further PN laws which would exclude them. The least general would be a version of (58). Since this refers to Cho arcs, it would, in contrast to the relevant principle for UN node-headed arcs (PN law 79), allow overrun 0 node-headed arcs to have employed arc local successors. If it turns out that overrun O node-headed arcs can never have employed local successors, one could propose instead (61) Overrun(A, B) AHeadLabel(O 1 A) -» Erase(A 1 B) . But as these questions require further research, we will not attempt to formalize further conditions here. It should be clear from this section that our major motivation for re­ jecting structures like (2b), that is, for allowing nonreplacer overrunning arcs to erase the arcs they overrun in some cases, is PN law 79. One can­ not consistently maintain this law and permit UN nodes to head Cho arcs. Thus, PN law 79 is one ground for weakening the "traditional" RG con­ ception of Cho arc distribution to allow erasing of some overrun arcs by their nonreplacer overrunners. However, the need for this weakening de­ rivable from PN law 79 is strengthened if some principle for O nodes like (58) or (61) can be incorporated as a PN law. For only the weakening of the conditions on Cho arcs to allow zeroing by overrunners preserves the possibility of situations in which an O node heads an arc which is over­ run by a nonreplacer and yet has no local successor.

9.5. Constraints on members of Inexplicit To conclude this chapter, we must point out a current weakness in our proposal to limit, via PN law 76, erasure of overrun arcs by nonreplacer overrunners to overrun arcs headed by members of Inexplicit. We have specified the membership of this set only by requiring that member nominal nodes be labeled O or UN, taking these symbols to be members of GNo . If left at this, however, the account would be nearly vacuous, for we have proposed no conditions limiting the class of nominal nodes which can be

9.5. CONSTRAINTS ON MEMBERS OF INEXPLICIT

397

labeled UN or 0 . Taken literally, we have imposed no real constraints on nonreplacer zeroing of overrun arcs. We have only required, contentlessly, that the head of an overrun arc erased by its nonreplacer overrunner be labeled 0 or UN. The problem is that nothing yet guarantees that nominals like John, the cat with two heads, most diapers, anarchist publications in Turkish, etc., cannot correspond to nominal nodes labeled UN or 0. Our intention is, evidently, that such nominals be incompatible with such labeling. Re­ quired then are PN laws which control labeling with O and UN in such a way that ordinary nominals like those at the head of this paragraph are in­ compatible with these categories. We are not in a position to provide an adequate set of such laws at the moment, a serious, but not, in our view critical limitation. The establishment of such laws depends, inter alia, on a serious analysis of the internal structure of nominals, an area we have not studied in detail. Thus, it is not surprising that much is left open at this early point of APG theory development. Moreover, lines of inquiry which will permit the relevant constraints to be tightened are par­ tially clear. Certain constraints are already discernible. One assumption we have made about both UN nodes and O nodes is that they correspond to existentially bound arguments. Given the definition of 'Binder Arc' above, we can express this by the requirement that all UN and O nodes be (i) heads of binder arcs, (ii) such that these binder arcs are neighbors of P arcs node-labeled 3. This condition immediately ex­ cludes many nominals from the class which can correspond to nominal nodes labeled O or UN : (62) PN Law 82 (The Inexplicit Binder Arc Law) a e Inexplicit -» (3A)(3B)(Binder Arc(A)AHead (a,Α) Λ Neighbor (Α,Β) Λ P arc (B) Λ Head Label (Ή,B)) . Note that as 'Binder Arc' was defined, the last conjunct of the consequent is technically unnecessary. We include it to allow for the more general

398

9. THE DISTRIBUTION OF CHO ARCS

definition of "Binder Arc" ultimately necessary, in which 3 will be only one of several possible quantifiers. Secondly, we observed that nodes included in Inexplicit are by and large semantically unspecified. It follows that a major constraint on such nodes is that they be incompatible with demonstratives, definite articles, numerals, lexical nouns, restrictive relative clauses, etc. It is in this area that the major limitations on Inexplicit lie. Unfortunately, it is rela­ tively obscure to us at this point how to impose such constraints, since we have not developed a formal account of internal nominal structures. We therefore leave this as a topic for future research. We make one final comment on membership in Inexplicit. We are assuming that all the conditions which determine membership in Inexplicit are part of universal grammar. Alternatively, one could assume that the universal constraints on membership are sufficiently weak that individual languages could have principles assigning nodes to Inexplicit. This course is undesirable and not to be adopted except under extreme pressure from the facts. Among its other consequences would be a severe weaken­ ing of the implications of The Nominal Arc Zeroing Law. We thus take it as a goal at this point to establish a rich enough set of PN laws so that individual grammars can have no effect on the membership of Inexplicit, guaranteeing the maximum content for The Nominal Arc Zeroing Law and insuring that, e.g., no language could have a sentence like (63) meaning "Melvin was shocked by 32 red-haired Italian demons": (63) Melvin was shocked. These would be permitted if, for instance, nominals of the form 32 redhaired Italian demons could correspond to nodes in Inexplicit.

9.6. Postscript: Further members of Inexplicit After nearly completing this manuscript, we observed certain sentences which suggest that heads of certain anaphoric arcs (see Chapter 11) may have to be granted membership in Inexplicit. The reason is that some such

9.6. FURTHER MEMBERS OF

399

INEXPLICIT

arcs must be permitted to be erased by arcs which overrun them. Consider: , f shaved \ (64) Ted I f J resse ^j in that tent. We must analyze these along the lines of our treatment of (5.53). Ted is the head of overlapping self-sponsoring 1 and 2 arcs, which cosponsor a 2 arc replacer erasing the 2 arc sponsor. The replacer then self-erases. So far, there are no new problems. However, examples like (64) have "pseudo-passive" correspondents of fair acceptability: (65) That tent has never been shaved in (by a prime minister). The problem is that, given current assumptions about fall-through, and the nature of passive clauses, it is impossible for the anaphoric replacer arc to self-erase in (65). For this would yield a violation of stratal uniqueness when the Loc arc headed by that tent has a 2 arc local successor, re­ quired by our conception of passivization. The only viable structure for (65) would seem to be:

(66)

Cho/

Cho,

Loc c I c Z Loc\c

MorqA· 3 (has) (never) (been)shaved

by

a prime minister

himself

that tent

there

Here C is the anaphoric replacer corresponding to the replacer in (5.53) which self-erases. However, C cannot self-erase in (66). If it did, it

400

9. THE DISTRIBUTION OF CHO ARCS

wouldhavecoordinates C 3 , C 4 , and C 5 , violating stratal uniqueness since the 2 arc E has

C3.

The natural solution for such cases is that

in (66), namely, to have the overrunning 2 arc, E, erase the 2 arc it overruns, as in previously discussed cases which, however, involved ana­ logues of C headed by 0 or UN nodes (see (ii) in note 27 of Chapter 8). However, for (66) to be compatible with PN law 76, the head of C must be a member of Inexplicit, although it is not an UN node or an 0 node. Our conclusion is that the class Inexplicit must be expanded to allow as members the heads of certain anaphoric arcs, perhaps only those of the "reflexive" type, a category which could be characterized by picking out those anaphoric arcs whose cosponsors are neighbors. This result, though incompatible with the detailed discussion in the earlier text, is not incom­ patible with its spirit, and does not undermine the conclusions or explana­ tions offered in any ways not directly obvious from the required changes in Inexplicit membership. Perhaps the most worrisome aspect of examples like (65) is that they lead to a class Inexplicit whose membership is formal­ ly diverse. We leave this problem for future work.

CHAPTER 10 GHOST ARCS AND DUMMY NOMINALS 10.1. Background The recent linguistic literature contains many references to dummy nominals, by which are meant such forms as those italicized in: (1) a. There are demons in Newark. b. It frightens me the things he does. 1 c. It is sleeting. d. It is obvious that Tricky was guilty. e. French Il Iui

est

arrive un malheur.

It to him/her is arrived a misfortune = "Something bad happened to him/her." f. German Es kamen zwei junge leute. It

came

two young people = "two young people came."

g. Welsh Yr oedd hi yn bwrw glaw ddoe. was she rain throw yesterday = "It was raining yesterday." The relevant phenomena in sentences like (1) have long been noticed. The term dummy (nominal) is, as far as we know, due to Jespersen (1937), who

Examples like (lb) are not to be confused with those like: (i) They frighten me, the things he does. (i) is an example of so-called right dislocation, the form they is an anaphoric pro­ noun not a dummy. Right dislocation is more productive than the dummy phenome­ non in (lb).

402

10. GHOST ARCS AND DUMMY NOMINALS

posited a special symbol in his system, s, to represent (certain) dummy nominals. Jespersen (1937: 92) 2 remarked about it like those in (Id): The chief reason for these symbols is practical convenience. The small s and ο are extremely handy for what I have elsewhere called preparatory it. This may be considered the real subject and object, respectively, in cases like "It is a great pleasure to see you" and "We have it in our power to do great harm", while the in­ finitive is put in extraposition (or, if you like, in apposition) at the end of the sentence. This may be written: S*V P(21) [*I0] —and S V 0* pl(S21) [*I02(21)].l It is, however, more convenient, and, by the way, more in ac­ cordance with the natural feeling of the unsophisticated mind, to look upon it as a mere preliminary or introductory word, a forebod­ ing of the real subject, "a dummy subject", and thus to write: s V P(21) S(IO) and SVo pl(S21) 0(I02(21)). Similarly when it prepares a whole clause as subject or object. The same remark holds good for the corresponding pronouns in other languages, il, ce, es, det, etc. Examples are found in Chapters 22-24. Although the concept Dummy Nominal is now familiar, there is no theo­ retical account of such elements in the linguistic literature, no published constraints on the conditions which a dummy nominal must/can meet, no "definition" of dummy nominal, no account of the relation between dummy nominals and sentence meanings. Although often observed that dummy nominals in a language L normally have a form identical to one of the weak definite anaphoric pronouns in L , there is no account which gives any insight into why dummy nominals behave in this respect like anaphoric nominals.3 2

Jespersen (1937: 92) made a distinction between nominals like those in (Ic) and (Id), which we regard as illusory. He did not characterize elements like the it in (Ic) as dummies, considering them to be the "real" subjects, apparently be­ cause there is no variant of such sentences without the pronoun, in contrast to those like (Id). We reject this view; see the discussion of (57a) and (58) in the text below.

3As far as we can determine, TG offers as a basis for the similarity between dummies and definite anaphoric pronouns nothing beyond the possibility of marking

10.1. BACKGROUND

403

We cannot present a complete treatment of dummy nominals here (see Perlmutter and Postal (to appear a, to appear c) for further discussion). But as the phenomenon interacts with some of our more basic assumptions, especially in the domains of coordinate assignment, Cho arcs, and grafts, we must sketch our underlying assumptions in this area.

10.2. Ghost arcs Our basic approach is that each dummy nominal corresponds to a nomi­ nal node which is the head of a certain kind of arc, referred to as a ghost arc. These will be a subset of the wider class of grafts called apparitions, defined as follows: (2) Def. 152: Apparition(A) Not( C 1 (A)) .

Proof. Direct consequence of The Ghost Status Theorem and The Self-

Sponsor Coordinate Law. QED. (6)

THEOREM

86 (The Ghost/L-graph Incompatibility Theorem) L-graph (X) a Ghost(A) -, A / X .

Proof. Direct consequence of The Ghost Status Theorem and the definition

of "L-graph." QED. Theorem 86 serves as a partial basis for explicating the commonly accept­ ed fact that dummy nominals have no meaning. Theorem 85 serves as a basis for explicating many properties of dummy nominal constructions. Given the notion Ghost Arc, one can introduce the notion Dummy Node. Dummy nodes are nodes which head some ghost arc. Then one can define the notion Dummy Arc as any structural arc whose head is a dummy node. Thus a ghost arc and all of its R-successors will be dummy arcs. All ghost arcs are dummy arcs but not conversely (e.g., the successor of a ghost arc is a dummy arc, but not a ghost arc). (7) Def. 154: Dummy (rtode)(a) *—> (3A) (Head (a, Α) Λ Ghost (A)) . (8) Def. 155: Dummy Arc (A) «-» Dummy node (Head (A)) AStructural (A) . The motivation for reference to the property Structural in (8) is that we do not want LP arcs which determine the linear ordering of dummy arc heads to be dummy arcs. However, some such arcs share heads with dummy arcs. See Chapter 12. A few words are in order about the kinds of elements which can corre­ spond to the heads of ghost arcs and hence dummy arcs. We want such arcs to reconstruct the notion Dummy Nominal. And it seems that all such entities should correspond to nodes labeled Nom. We could guarantee this by directly stipulating that the head of every ghost arc is labeled Nom. However, it is doubtful that this is the way to proceed.

10.2. GHOST ARCS

405

For ghost arcs are grafts, hence entrants. And PN law 29, The Central Arc Head Label Law, of Chapter 7 says that entrant Central arcs are head labeled Nom if their heads are not labeled Cl. Therefore, one can guaran­ tee the required restriction of ghost heads to nominals if (i) all ghost arcs are Central arcs; and (ii) it is precluded that the head of a ghost arc be labeled Cl. The former condition is met, since, adopting an RG insight, we restrict, with one irrelevant exception, all dummy arcs to a subset of Central arcs (see PN law 87 below). So far though nothing guarantees (ii). (ii) would be imposed if it were impossible for the head of any graft to be labeled Cl. This seems generally true. However, in Chapter 13 we encounter one class of structures where it seems necessary to allow graft heads to be labeled Cl. It is possible to show that ghost arcs would meet the antecedents for a law limiting Cl labeling to this special class, thus preventing ghost heads from being labeled Cl. However, this would in­ volve us prematurely in the considerations of Chapter 13. Therefore, we adopt, probably unnecessarily, a weaker statement at this point. We claim that it is impossible for the head of any Nominal arc graft to be labeled Cl: (9) PN Law 83 (The Nominal Arc Graft Head Labeling Law) Nominal arc (A)

Λ

Graft(A)

Not (Head Label(Cl j A)) .

From (9) and PN law 87 below, one can prove that every ghost arc is head labeled Nom, and thus that every dummy arc is (see Theorems 94 and 95 below). We thus take it at this stage that all dummies are nominal nodes. Although ghost arcs are by definition grafts, the class of dummy arcs completely crossclassifies the typology of domestic arc, immigrant arc, and graft. All and only those dummy arcs which are ghost arcs are grafts; all and only those dummy arcs which are local successors of other dummy arcs are domestic arcs; and all and only those dummy arcs which are foreign successors of other dummy arcs are immigrant arcs. 10.3. The basic constraint on ghost arcs Our fundamental claim about ghost arcs is that these meet a strict con­ dition linking them to their sponsors. Namely, every ghost arc, G , must

406

10. GHOST ARCS AND DUMMY NOMINALS

have an R-Successor which (i) is a neighbor of G's sponsor, and (ii) has the same R-sign as G's sponsor. The relevant constraint is definable in terms of the concept Facsimile, which we recall from Chapter 5: (10) Def. 82: Facsimile (A, B) «-» Local Same-Sign (A, B) . We can then state: (11) PN Law 84 (The Ghost Arc Law) Ghost(A) Λ Sponsor (Β, A) -» (3C)(R-Successor(C,A)

Λ

Facsimile (C,B)) .

This restriction means that every dummy nominal must head an arc which is a facsimile of the arc sponsoring the ghost arc which determines that nominal's existence. There are two different ways in which a condition like that in (11) can be met. First, taking account of the reflexive character of ancestrals like R-Successor, PN law 84 would be met if the ghost arc itself were a fac­ simile of its sponsor. We refer to ghost arcs of this type as stable ghost arcs, and to their heads as stable dummies. We also introduce the comple­ ments of these notions within the relevant sets in the obvious way. (12) a. Def. 156: Stable (Ghost (arc)) (A) «-» ((VB) (Sponsor (B,A) -> Facsimile (A,B))) . b. Def. 157: Unstable (Ghost (arc)) (A) «-» Ghost (A) Λ Not (Stable (A)) . (13) a. Def. 158: [Stable Dummy (a) 1 ί Stable (A) | { }—(3A)(Head(a,A) A { [). b. Def. 159: [Unstable Dummy (a) ι IlJnstable(A)I We illustrate stable dummies and, more generally, begin to illustrate how the apparatus involving ghost arcs constructed so far applies to actual natural language cases of dummy nominals by examining English "extraposition" constructions like that in (14b): (14) a. That Ted lost worries me. b. It worries me that Ted lost.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

407

We adopt the basic RG insight, which is, in APG terms, that cases like (14b) share the self-sponsoring arcs of those like (14a) but differ in the arcs involving and induced by the dummy nominal it. We regard it as corre­ sponding to the head of a 1 arc, which correlates with the fact that the correspondent of the head of the initial 1 arc, the complement clause, is the head of a Cho arc. This follows from The Chomeur Law, given that the ghost arc overruns the 1 arc headed by the complement (see below). The chomeur status of the complement is manifested most clearly by its post verbal order, typical of nominals corresponding to final stratum Cho arc heads in English. 4 In the present framework, we then analyze examples like (14b) as in­ volving a 1 arc headed by a dummy which overruns the initial 1 arc. The Chomeur Law and The Nominal Arc Zeroing Law then force the initial 1 arc to sponsor a local Cho arc successor. The Cho Arc Cosponsor Law and The Cho Arc Second Sponsor Identity Law, PN laws 60 and 61, require in addition that the ghost arc also sponsor the Cho arc. Hence a repre­ sentation for (14b) in these terms would be as follows, where here and be­ low, for convenience, we use a triangle to represent the entire complement clause, since its internal structure does not concern us here. 5

4 More precisely, typical of shallow Cho arc heads. See Chapter 12. 5The existence of stable ghost arcs like A in (15) is, in our view, a reason for doubting the existence of so-called "spontaneous demotion" in the sense of Comrie (1977), Keenan (1975), and Jain (1977). In our terms, this situation, ex­ cluded in Chapter 8 by The Chomeur Law, involves a local Cho arc successor for a Term arc which is not overrun. That is, "spontaneous demotion" would permit, e.g., a 1 arc to have a local Cho arc successor without the need for any other 1 arc to occupy the first stratum of that Cho arc. However, the mechanism of stable ghost arcs permits a Termx arc to "provide itself with" a Cho arc successor with­ out the need for any nonghost Termx arc to exist. Moreover, if this possibility is combined with self-erasure for the ghost arc, all of the effects sought by the de­ scription in terms of "spontaneous demotion" are achieved without weakening the current theory (in particular, with no weakening of The Chomeur Law). Given a case like:

408

10. GHOST ARCS AND DUMMY NOMINALS

(15)

worries

(15) involves the pair Sponsor(C, A) , which we have not discussed. Since all arcs require sponsors, we know a priori that A must have some sponsor. And since we want it to be a ghost arc, it must have a nonoverlapping sponsor. In this case, it seems natural to take C to be the spon­ sor of

A , since it is the constituent whose point is the head of C which

determines the possibility of the construction. As is well known, this must be a complement constituent, and one of a restricted type, which need not concern us at this level of discussion. We return to the question of ghost arc sponsors below. A key feature of (15) is the coordinate C3 on the ghost arc A . That this is A's first coordinate follows from The Ghost Coordinate Law, briefly mentioned in Chapter 6: (16) PN Law 24 (The Ghost Coordinate Law) Ghost(A)

Λ

Local Sponsor (Β,Α) Λ

< CJT

/3 >(B) -»

(A) ·

d the initial 1 arc vanishes from the S-graph, the initial 1 is a surface chomeur, and there is no visible surface 1 , although no current APG laws are violated (in particular, The Final 1 Law and The Chomeur Law are not).

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

409

This requires that the first coordinate index of a ghost arc with a local sponsor be +1 of the first coordinate index of its local sponsor. PN law 24 gives the right result in (15). But the same result would follow if instead the principle referred to the index of the last coordinate of the local sponsor of a ghost, since, in (15), the first and last coordinates of the ghost's local sponsor are identical. However, we showed in Chapter 6 that such a formulation was insufficient for other types of ghost arc than that in (15), types to which we return presently. One obvious consequence of PN law 24 is that no ghost arc can appear in a stratum earlier than the first stratum of its local sponsor. In this re­ spect, ghost arcs are like local successors, replacers, and immigrant arcs, which also cannot appear earlier than their local sponsors. 6 ' 7 The ghost arc, A , in (15) overruns its local sponsor. The question arises whether this is an accident. Can there be stable ghost arcs which do not overrun their sponsors? The answer is negative: (17) THEOREM 87 (The Stable Ghost Overrun Theorem)' S t a b t e ( A ) Λ Sponsor(B, A) h> O v e r r u n ( A t B ) . Proof. Let A' be stable and B' be its sponsor. Assume (B / ).

Since A' is a facsimile of B', Local Sponsor(B', A') . The Ghost Coordi­ nate Law then specifies that < c jj +1 y >(A') and hence A' overruns B'. QED. Thus the fact that the stable ghost, A , in (15) has a local sponsor which it overruns is lawful. And the fact that A is a facsimile of its local sponsor reveals the obvious relationship: ^More precisely, it is immediately obvious only that replacers cannot appear in a stratum earlier than that of their facsimile sponsor, for only this is guaranteed by The Replacer Coordinate Law. However, it will, we suspect, ultimately turn out (though this is not guaranteed yet since we have imposed no precise constraints on replacer cosponsors) that if a replacer has two local sponsors, either these are both c^ arcs or the nonfacsimile sponsor is a successor of the facsimile sponsor, and hence has a later first coordinate index.

7One would

like to ultimately prove as a theorem that no arc can appear in an earlier stratum than any of its local sponsors. See note 5 of Chapter 6.

410

10. GHOST ARCS ANP DUMMY NOMINALS

(18) THEOREM 88 (The Overran Facsimile Theorem) Overrun(A1B) -» Facsimile(A,B) . Proof. Immediate from the definitions of "Overrun" and "Facsimile" ("Local Same-Sign"). QED. Thus, as a consequence of Theorem 88, all ghost arcs which overrun their sponsors, that is, given Theorem 87, all stable ghosts, satisfy The Ghost Arc Law independently of whether they have successors or not. This is a partial justification for the choice of the term "Stable." Further justification for this terminology, in particular, for the con­ trasting "Unstable," derives from:

(19) THEOREM 89 (The Unstable Ghost Theorem) Unstable(A) -» (3B)(Soccessor(B, A)) . Proof, Let A' be unstable. It follows from the definitions of "Stable" and "Unstable" that A' is not a facsimile of its sponsor. But The Ghost Arc Law determines that there is some arc, call it C', which is an R-successor of A' and which is a facsimile of the sponsor of A'. Since this R-successor is not A' itself, C' must be a D-R-successor of A'. But a D-R-successor of an arc D' is an R-successor of a successor of D', and hence D' has a successor. QED. Hence the justification for the term "Unstable" is that an unstable ghost must have a successor. Therefore:

(20) THEOREM 90 (The Unstable Ghost Nonsurface Arc Theorem) Unstable(A)

Not (Surface Arc(A)) .

Proof. Immediate from The Unstable Ghost Theorem and Theorem 8, The Predecessor Nonsurface Arc Theorem. QED. In other words, an invariant property of unstable ghost arcs is their non­ occurrence in S-graphs, which serves in part to disguise their existence.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

411

Let us now illustrate what we take to be an instance of an unstable ghost arc. We consider again instances of German impersonal passive clauses:

— (Sf)O occurred" Such clauses show the superficial properties of passives in German (see Breckenridge [1975] for the relevant parallelisms), i.e., they have the standard passive auxiliary, and passive verbal morphology. Moreover, where the initial 1 shows up, it occurs in a von phrase, as does the initial 1 of a personal passive. In our terms, clauses like (21) then have a struc­ ture of the form:

es

(wurde) geloufert

We here adopt, adapting to our terms, the basic stage 2 RG analysis of impersonal passive clauses (see Perlmutter and Postal [to appear b, to appear c]). The essence of this is that the dummy nominal is a 2 (as well as a 1) and thus subject to passivization like any other 2.8 This explains why examples like (21) have the expected properties of passive clauses in German, as argued by Breckenridge(1975), i.e., the facts of Q

Comrie (1977) considers several alternative analyses of impersonal passives. However, one where a dummy node bears both the 2 and 1 relations is not among them.

412

10. GHOST ARCS AND DUMMY NOMINALS

auxiliary choice, verbal morphology, and chomeur marking (when there is a chomeur), as remarked earlier. Structures like (22) reveal why The Ghost Coordinate Law cannot tefet to the last coordinate of the local sponsors of ghosts. For in (22) the first coordinate index of the ghost is identical to the last coordinate index of its local sponsor, that is, we want the sponsor to fall through into the c 2 nd stratum, creating an accusative situation as in standard, personal passive constructions. More generally, given reference to the last coordi­ nate, there would be two possibilities: (i) the last coordinate of A in (22) would be C 1 ; (ii) the last coordinate of A in (22) would be C 2 . If (i), then no accusative stratum results but, more fundamentally, given The Fall-Through Law, A can fail to fall through only if A has a local assassin in C2 · And it has no such motivated assassin. Hence (i) is not a tolerable analysis. If (ii), A has fallen through into C 2 and again no accusative stratum results. Worse, no well-formed PN results, since the c 2 stratum in this case is unmotivated and the fall-through for A is il­ legitimate. Parallelremarksholdifthelastcoordinateof A is C 3 , C 4 , etc. Hence, in cases like (22), that is, in cases of locally sponsored un­ stable ghosts, it is not possible for the ghost arc to take its first coordi­ nate from the last coordinate of its local sponsor. We conclude tentatively that it is the first coordinate index of the local sponsor of a ghost arc which lawfully determines its first coordinate index. 9 Comparing (22) to (15) above, the contrast between unstable and stable ghost arcs emerges. C in (22) is not a facsimile of its sponsor A , and is hence unstable. Theorem 89, The Unstable Ghost Theorem, requires that C must have a successor, which it does. This feature of examples like (22) exemplifies a fundamental property of such impersonal constructions, one which has confused the analysis of such structures in the past. Q

It is not clear that PN law 24 is the correct coordinate law for ghost arcs. It may ultimately be necessary to specify a somewhat more complicated law which would give ghost arcs first coordinate indices greater than the first coordinate in­ dices of any of their facsimiles.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

413

Let us ask what would happen if no passivization was involved in cases like (21). Or, in different terms, since passives generally have active correspondents, what are the active correspondents of passive clauses like (21)? This question is closely related to an objection almost inevitably raised whenever an analysis of sentences like the RG treatment of (21), embodied in APG terms in (22), is proposed. The objection is that (i) there is no "direct" evidence that the dummy is on a 2 arc since, with respect to the more immediately available S-graph, the dummy is obvious­ ly the head of a 1 arc; and (ii) examples in which the dummy would "really" be the head of a 2 arc, that is, the head of a surface 2 arc, are ill-formed. For it is well known that intransitive clauses in German do not permit dummy 2s , and hence examples like (21) have no active correspondents: Man I I lauft I

I I Irk I« h (Hansj (laughs)

The previous RG claim was that not only are examples like (23) illformed in German, but that the analogues would be ill-formed in any lan­ guage. We agree with this view and claim that Theorem 89 justifies it. For, in the terms developed so far, an example of the form in (23) would involve a PN of the form: (24)

Man

0

However, B in (24) is an unstable ghost arc and thus, via Theorem 89, must have a successor, which it does not have. Hence (24) is blocked

414

10. GHOST ARCS AND DUMMY NOMINALS

with no need for ad hoc rules in German, and similarly for other languages with the analogous facts. (22) is well formed because passivization pro­ vides the unstable ghost arc with a (1 arc local) successor. Given Theorem 89, which is provable from The Ghost Arc Law, struc­ tures like (24) are universally blocked. Therefore, one can keep an analy­ sis of examples like (21) of the form in (22), permitting capture of all the similarities of such clauses to personal passives, without ad hoc languageparticular statements to block examples like (23). In a theory embodying The Ghost Arc Law, and hence Theorem 89, the fact that impersonal pas­ sives have no active correspondents is predicted not only for German but for all languages manifesting this clause type. The absence of such actives is thus no argument against the original RG analysis of such clauses, as adapted here. Having a successor is a necessary condition for an unstable ghost arc, given The Ghost Arc Law. However, this is not at all sufficient. For ex­ ample, our conception of nominal flagging (see Chapter 13), the description of prepositions, postpositions, etc., requires the arc determining the flag to have a (Marq arc) successor. We now show that the presence of such a flagging structure in association with an unstable ghost arc does not suf­ fice to keep such arcs consistent with The Ghost Arc Law. Consider a hypothetical language otherwise like German except that 2s are flagged with the preposition gu. This would yield potential sen­ tences like (23) of the form: (25) Hypothetical German-like Sentence Hans lauft gu es In our terms, such examples would have the representation:

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

Hans

es

gu

415

Iauft

Here B is the unstable ghost arc, which has a Marq arc successor, E , under our conception of flagging as involving replacers like C cosponsored by an arc (B) and its Marq arc successor (E), in accord with one general type of replace situation. The existence of E thus guarantees that (26), in contrast to (24), is consistent with The Unstable Ghost Theorem. However, (26) is still not a possible well-formed PN in any natural language, given The Ghost Arc Law, since the ghost arc B has no R-successor which is a facsimile of B's sponsor, A . PNs (15) and (22) are typical cases of ghost arc structures, one stable, the other unstable. In both, the following condition is met: (27) Ghost(A) ASponsor(BlA)

(3C)(R-Successor(C,A)AOverrun(C,B)) .

The question arises whether this condition, which is stronger than, and hence entails, The Ghost Arc Law, is a truth which should be imposed on universal grammar. By specifying The Ghost Arc Law as a PN law, we implicitly assumed that this was not the case. Our reasons are that, al­ though (27) is met in many cases (given Theorem 87, in all stable ghost cases), in fact, in a strong majority of cases, there may nonetheless be

416

10. GHOST ARCS AND DUMMY NOMINALS

examples of ghost arcs which contradict (27), although not The Ghost Arc Law. The examples in question involve a type of clause found in a number of languages including Georgian and Russian. These clauses involve in­ version, that is, 3 arc local successors for 1 arcs, where the 1 arcs in question are neighbors of P arcs whose heads correspond to intransitive verbs. In these clauses, the only self-sponsoring Nuclear Term arcs have 3 arc successors. If nothing else is specified, such clauses will violate, inter alia, PN laws 44 and 47, The Final 1 Arc Law and The Nuclear Term Stratal Continuity Law. Since the sentences exist, we predict on the basis of these laws that something else does "happen." Our claim is that this "something else" is the existence of an (unstable) ghost arc sponsored by the 1 arc predecessor of the 3 arc due to inversion. The Unstable Ghost Arc Theorem requires that this ghost arc have a successor. However, there are reasons to doubt whether this successor can overrun

the sponsor of the ghost arc. An illustration of the construction in question is, as insightfully noted by Perlmutter (to appear d), the following example from Russian: (28) emu

ne

him _ not Dative

spitsja sleep-reflexive = "He can't (get to) sleep."

The dative marking of emu is the initial basis for taking this nominal to correspond to the head of a final stratum 3 arc. The meaning and paral­ lelism with noninversion examples like (29) are further bases for this assumption: (29) on

ne

spit

he „ . not sleep = "He is not sleeping, does not sleep." Nominative Grammatical arguments for an inversion treatment of examples like (28) based on facts like reflexivization are given in Perlmutter (to appear d). If, however, the initial 1 arcs of intransitive clauses have 3 arc succes­ sors, then, unless something else "happens," violations will ensue of PN laws 44 and 47.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

417

Our claim is that, in spite of inversion, examples like (28) do not con­ tradict either of these laws because of the existence in such clauses of dummy nominals (and hence ghost arcs): (30)

emu

α

b

sja

spit

Here B is the initial 1 arc with 3 arc local successor, A , defining an inversion clause. D is the (unstable) ghost arc sponsored by B . Without D , the c 2 nd stratum would contain no Nuclear Term arc, violating The Nuclear Term Arc Stratal Continuity Law. D then has a 1 arc local suc­ cessor, as determined by The Unaccusative Law, since it is unaccusative at c 2 . Our claim is that the 1 arc successor of D , C , self-erases, accounting for the invisibility of the dummy in the actual sentence. All dummies in Russian are apparently invisible. See Comrie (1974a) for some discussion interpretable along these lines. E here is a replacer of the "copy arc" type (see Chapter 11), required in this construction in Russian. This arc sponsors a clitic arc in the verb, whose head corresponds to the reflexive particle sya, this arc foreign zeroing its sponsor (consistent with The Nominal Arc Zeroing Law). It might be claimed that postulation of the ghost arc/dummy nominal structure for cases like (28) is an empirically unmotivated act of despera­ tion to preserve The Final 1 Arc Law and The Nuclear Term Stratal Con­ tinuity Law. However, this is incorrect. Even though the dummy arcs in (28) are not surface arcs and hence the dummy nominal is erased, there is evidence for this invisible dummy, as in many other cases of such. In

418

10. GHOST ARCS AND DUMMY NOMINALS

particular, only postulation of the dummy seems to provide a non ad hoc way of accounting for the reflexive form of the verb, via the standard "copying" mechanism often associated with 1 arc local successors of 2 arcs. 10 Secondly, as predicted by the analysis in (28), and more deeply, as predicted by The Final 1 Arc Law, examples like (28) are, as noted by Perlmutter, embeddable as complements in contexts where the final stratum complement 1 must raise. As predicted, clauses like (28) act with respect to raising as if they had final Is: (31) emu him _

dolzno

spokojno

should peacefully 3rd sing, neuter

spat'sja sleep-reflexive

doma at home =

"He should be sleeping peacefully at home." Here dolzno is a raising trigger, forming constructions which normally re­ quire a final 1 in the complement. Postulation of the dummy nominal meets this condition as well as providing a basis for the third person in­ flection of dolzno. This kind of raising test often provides evidence for invisible dummy nominals, in accord with the predictions of, inter alia, The Final 1 Arc Law. Returning to (30), D is an unstable ghost arc, and one with an R-successor which is a facsimile of D's sponsor, as required by The Ghost Arc Law. However, this R-successor, C , does not overrun the sponsor of

D, B,

since

B 's

last coordinate is C1 and C's first

coordinate is C3 , as guaranteed by the inversion analysis and The Ghost Coordinate Law. Hence, if structures like (30) are correct for the relevant Russian construction (and for the analogue in Georgian), it is not possible to strengthen The Ghost Arc Law to (27). No constraints on ghost arcs or other conditions on PNs we have im­ posed so far would block an analysis otherwise like (30) in which, however, ^An explanation of the parallelism between "ordinary" reflexives and reflex­ ive passives is offered in Chapter 11, section 8.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

419

the ghost arc sponsored by B was a 1 arc, hence stable, yielding a par­ tial structure:

emu

α

(32) has most of the virtues of (30), except one. It provides no general basis for the reflexivity of the construction, which depends on the exis­ tence of a 2 arc. However, no principles so far imposed preclude (32), and such structures would permit a strengthening of The Ghost Arc Law. Hence, it is initially tempting to consider (32) correct and to seek some other explanation for the reflexive character of the Russian construction. However, counterbalancing this, structures like (32) are inconsistent with a further law about stable ghost arcs proposed below in this chapter, PN law 85. This has considerable independent appeal and its maintenance seems to us to outweigh the virtues of strengthening The Ghost Arc Law to (27). To a certain extent, however, the matter should be regarded as open. Were there to turn out to be no PNs like (30), then evidently one can require that every ghost arc have an R-successor which overruns the sponsor of that ghost arc. 11 11 Even (27) is weaker than a principle at one time assumed in RG. This was that every dummy nominal has to "create a chomeur." Translating into APG terms, this would say:

(i)

Ghost(A) -» (3B)(3C)(R-Successor (B 1 A)ACho arc (C)ADomestic (C) A Spawns (B 1 C)).

For the definition of 'Spawns', see (66) below. (27) is weaker than (i) in rougjily the way The Chomeur Law is weaker than RG assumptions about chomeurhood. (27) only requires that a ghost arc have an R-successor which overruns the ghost sponsor. It would not require the latter to have a Cho arc successor, since The Chomeur Law allows other possibilities for overrun arcs (but cf. the discussion of (54) in the text).

420

10. GHOST ARCS AND DUMMY NOMINALS

The Ghost Arc Law requires that each ghost arc have an R-successor which is a facsimile of the sponsor of that ghost arc. In (15), (22), and (30) an even stronger condition is met: the facsimile of the ghost arc sponsor is a neighbor of the ghost arc. All of these structures illustrate the pattern: (33) Ghost(A)ASponsor(B j A) -> (3C) (R-Successor (C 1 A)

Λ

Facsimile(C 7 B) ANeighbor(C j A)) . In these cases, the ghost, its sponsor, and the facsimile of the sponsor are all neighbors. In other words, the sponsor of the ghost is a local sponsor. One should ask whether (33) is accidental or whether the extra strength in (33) as against The Ghost Arc Law should be imposed as a PN law (rendering The Ghost Arc Law a trivial theorem). However, while (33) seems true in an overwhelming majority of cases, there are reasons to suspect that it is too strong to be imposed as a PN law. These reasons are an important basis why we have not required, more generally, that all structural grafts have local sponsors. While most ghost arcs seem to have local sponsors, Breckenridge (1975) has studied a class of impersonal object-raising constructions in German. As far as we can see, these can only be analyzed in current terms, that is, consistently with The Ghost Arc Law, as involving subordinate clause un­ stable ghost arcs whose successors are in main clauses. Examples would be: (34) a. Dem Spion war schwer the dative spy was hard

zu to

folgen. follow

b. Es war dem Spion schwer zu folgen. = "It was hard to follow the spy·" We would analyze both (34a, b) as involving main clause dummy arcs, with (34a) involving self-erasure of the dummy arc. However, since these are, as Breckenridge argues, object-raising constructions, the main clause dummy arc in question is the immigrant arc successor of a ghost arc in the complement clause.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

421

Translating her analysis into APG terms, and making some additional assumptions, examples like (34) would involve the partial representation in (35). The key point is that in German only 2s are subject to object raising, motivating the postulation of a downstairs ghost 2 arc in the same way that such are motivated in impersonal passives: (35)

(war) schwer

(zu) folgen

We take this structure to involve upstairs inversion and raising of the downstairs 2 to be an upstairs 2 , it becoming an upstairs 1 via The Unaccusative Law. The key point is that clauses based on the verb folgen take as objects only final stratum 3s and thus, without dummies, are not suitable for being "object-raising" complements. In this case, however, the ghost arc, I, is sponsored by the main clause C 1 2 arc, E, which I's successor, B, overruns. This leads to a Cho arc successor for E. I provides the complement clause with the 2 arc it requires to be an "object-raising" complement. With respect to current assumptions, the key property of a ghost arc like I in (35) is that it can maintain consistency with The Ghost Arc Law only if it has a foreign sponsor. I is not a facsimile of any arc in the complement and has no local successor. However, B , which is I's suc­ cessor, is a facsimile of I's (foreign) sponsor, E , keeping the structure consistent with The Ghost Arc Law. We conclude that some ghost arcs have foreign sponsors.

422

10. GHOST ARCS AND DUMMY NOMINALS

A notable feature of structures like (35) is that the ghost arc, there I, does not meet the antecedent conditions of PN law 24, The Ghost Coordi­ nate Law. Hence, its first coordinate is not determined by that law. How­ ever, arcs like I do meet the conditions of PN law 25, The Graft Coordi­ nate Law, which specifies that all arcs (these are necessarily grafts) not having local sponsors have c 2 for their first coordinate. Thus, a conse­ quence of the present framework is that all ghost arcs without local spon­ sors are arcs. As in the case of the German impersonal passives in (21), the current system predicts that impersonal object-raising constructions like (35) will not have correspondents in which the ghost arc exists but no object raising is present. The reason is that the ghost arc is unstable. Hence, it must have a successor and, moreover, an R-successor which is a facsimile of its sponsor, that is, the upstairs 2 arc. Consequently, the ghost arc can exist in such cases only if it has the immigrant arc successor determined by the object-raising construction. No ad hoc rules are needed to block the case where it has no such successor. Complicated as (35) might seem, we suspect that the real structure of examples like (34) is even more complicated. In particular, we suspect that these involve in addition all of the structure defining a clause union construction, which, as discussed in Chapter 8, section 6, guarantees that arcs J and M in (35) would have main clause successors (J would have a Dead arc successor). We conclude that (33) is too strong and hence that some ghost arcs have foreign sponsors. More generally, it is impossible to require all structural grafts (and hence all structural arcs) to have local sponsors. 12 However, one's conclusions in this area must be tentative. The examples discussed by Breckenridge (1975) are the only cases known to us where there seems ground for postulating foreign sponsored ghost arcs. In view 12 If all structural grafts have local sponsors, then all structural arcs do. For domestic arcs have such by definition and immigrant arcs have them because of PN law 12.

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

423

of this limited evidence, confidence in the existence of such must remain restricted. We stress, however, that postulating such sponsors causes no difficulty for The Ghost Arc Law, which is, beyond The Ghost Coordinate Law, the fundamental constraint imposed on ghost arcs. 13 We have illustrated several cases where an unstable ghost arc fails to have an R-successor which is a facsimile of the ghost sponsor, yielding ill-formedness with no need for special grammatical rules. There are cases of this sort even when the ghost arc in question overruns another arc. Consider the German example in (36a) treated in Chapter 9, represent­ ed in (36b): (36) a. Es wurde

gegessen.

It became eaten = "UN ate UN." b.

UN

es

UN (wurde) gegessen

The verb essen is transitive, and thus we take (36) to involve a selfsponsoring 2 arc headed by an UN node. The ghost arc required for the impersonal passive construction will overrun that self-sponsoring 2 arc. However, (36a) no more has an active correspondent than the intransitive case in (21) above. This is predicted since, although the ghost arc C in (36b) overruns and is hence a facsimile of D , it is not sponsored by D . Hence, this property does not keep C from needing an R-successor which is a facsimile of A , a condition that cannot be met in an active correspondent of (36b). 13 These foreign sponsored ghost cases are consistent with (27) as well as with The Ghost Arc Law.

424

10. GHOST ARCS AND DUMMY NOMINALS

In (36b), C not only overruns D , it assassinates (zeroes) it, in accord with both PN laws 76 and 79, The Nominal Arc Zeroing Law and The UN Node-Headed Arc Limitation Law. A priori one would predict that German sentences parallel to (36b) could exist in which the self-sponsoring 2 arc was headed by a node not in Inexplicit, requiring this arc to have a Cho arc local successor. However, this seems not to happen: (37) *Es

wurde

das Fleisch gegessen.

It becomes the

meat eaten = "UN ate the meat."

In some languages, we would predict facts like (37) by requiring that the impersonal passive ghost arc not overrun another 2 arc, limiting imperson­ al passives to intransitive structures. However, this would also block (36a). It seems that the restriction in German is that the ghost arc in an impersonal passive cannot be the sponsor of a Cho arc. This allows just that class of cases in which the ghost arc itself erases the 2 arc deter­ mining the prior transitivity of the structure. In other languages, impersonal passives are possible with a richer class of transitive structures. This is probably the case in Spanish, 14 where the impersonal passive construction is reflexive in character. Both (38a, b) exist, the latter having the structure in (38c). In our terms, the a marked nominal tos adores is a chomeur in (38b):

(38) a. Se

ve bien desde la galeria.

self see well from the balcony = "0 can see UN well from the balcony." b. No

se

oia

bien a Ios actores.

not self hear well to the actors = "0 couldn't hear the actors well."

14 The hedge is due to the fact that it is not completely clear that examples like (38) are impersonal passives. We are indebted to D. Perlmutter for discussion of this matter. He is, however, in no way to be blamed for any of the claims rele­ vant to such cases.

425

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

c.

0

(a) Ios actores

el

ellos

se

ofa

Here E is the ghost arc sponsored by A , and having its first coordinate index properly equal to +1 of A's first coordinate index. Moreover, E has an R-successor which is a facsimile of A, namely, D , the 1 arc characterizing passivization. Since E overruns C and does not erase it (could not erase it, given The Nominal Arc Zeroing Law) and C has no other employed assassin, C must have a Cho arc local successor. It does have one, B , cosponsored by the overrunner, the ghost arc E , in accord with the principles of section 2 of Chapter 8- G is the "copy arc" (see Chapter 11, section 6) required by the fact that the construction in question is a reflexive passive. In Spanish, reflexive 2s yield verbal clitics of the form se, represented by the pair Sponsor (G, I). A key feature of (38c) is that although E overruns C , C does not sponsor E . E is therefore unstable. Hence, it must have a successor and, as in earlier cases, there will be no active correspondent of reflexive impersonal passives like (38a, b), given The Ghost Arc Law. Cases like (36a) and (38b) stress the point that the division between stable and un­ stable ghosts does not correlate directly with whether or not a ghost over­ runs some arc. While it is true that all stable ghost arcs overrun an arc

426

10. GHOST ARCS AND DUMMY NOMINALS

(see Theorem 87), unstable ghost arcs may or may not be overrunners. The only sure conclusion is that no unstable ghost arc overruns its own spon­ sor, for this would, contradictorily, make it stable. In cases so far illustrated like (15) above, stable ghost arcs have al­ ways sponsored (organic) Cho arcs. But so far nothing guarantees that this is lawful. Allowing stable ghosts not to sponsor organic Cho arcs permits, inter alia, structures like (9.33), repeated as (39a), and also per­ mits those like (39b):

there

UN

exist

b,

Joe

it

Mary

(was) tickled

c. Joe was tickled it by Mary. Structures like (39b) would give rise to strange and unattested passives like (39c). In this, C is a ghost arc, consistent with The Ghost Arc Law since it is a facsimile of its sponsor, B, and hence stable. Unlike other attested stable ghost arcs, C does not sponsor a domestic Cho arc. We suspect sentences like (39c) are impossible in any language and take it as no accident that attested stable ghost arcs sponsor domestic Cho arcs:

10.3. THE BASIC CONSTRAINT ON GHOST ARCS

427

(40) PN Law 85 (The Stable Ghost Arc Sponsor Law) Stable(A) -> (ΉΒ)(Sponsor(A, B)a C1io arc(B)ADomestic(B)) . (40) blocks structures like (39a, b). In the former case, this is desirable since, as Chapter 9 indicates, there are several other possible structures for the relevant sentences. And in cases like (39c), it is fine because these are unattested. As a consequence of PN law 85, all ghost arcs must sponsor organic arcs. (40) stipulates this directly for stable ghosts, and it is required by Theorem 89, The Unstable Ghost Theorem, that unstable ghosts have suc­ cessors and hence that they sponsor organic arcs. A further empirical consequence of The Stable Ghost Arc Sponsor Law is that it eliminates one of the two possible structures for the dummy nominal in intransitive inversion cases like (28) above. PN law 85 blocks a stable ghost structure like (32) above, leaving only the unstable ghost representation in (30). This, we recall, is more desirable because it lays the basis for explaining the reflexive form of the construction. Similarly, The Stable Ghost Arc Sponsor Law precludes examples like (41a) with a structure of the form (41b): (41) a. Melvin ate it.

C1C2 Melvin

UN

ate

Here C is a stable ghost and compatible with The Ghost Arc Law since it is a facsimile of its sponsor. But structures like (41a) with dummy nominal readings, i.e., meanings like 'iMelvin ate" are predicted to be im­ possible by The Stable Ghost Arc Sponsor Law. The latter then has a range of desirable predictions and appears relatively well supported.

428

10. GHOST ARCS AND DUMMY NOMINALS

10.4. Constraints on ghost arc sponsors and dummy arcs We have so far imposed no particular constraints on the sponsors of ghost arcs, observing that it was apparently necessary to allow both local and foreign sponsors for these. However, judging by the cases known to us, rather strict constraints exist on such sponsors. One is that a ghost arc sponsor must be organic: (42) PN Law 86 (The Ghost Sponsor Organicity Law) Ghost (A) Λ Sponsor (B, A) -> Organic (B) . This precludes, e.g., the possibility that a replacer could sponsor a ghost or that one ghost could sponsor another. Neither PN law 86 nor any previous statement imposes constraints on the R-signs of either ghost sponsors, ghosts, or R-successors of ghosts. Our impression, however, is that all these are highly restricted with re­ spect to R-sign. There is an RG principle in this area (see Perlmutter and Postal [to appear a]) which claims, when translated into APG terms, that: (43) Dummy arc (A)

Nuclear Term arc (A) .

(43) trivially entails that ghost arcs are Nuclear Term arcs. However, although (43) is elegant and largely correct, it is not incorporable as such into the current theory. What seems right about (43) and what motivated its RG forerunner, is the absence of attested dummy arcs which are: (i) Cho arcs, (ii) Dead arcs, (iii) Oblique arcs, (iv) 3 arcs, or (v) Overlay arcs. Perhaps the most interesting implication of (43) is (i), which has directly testable consequences. For instance, as long noted in unpublished RG work, the principle in question explains the impossibility of English passives like (44b, i, ii) corresponding to (44a): (44) a. It bothers me that he lied. b. (i) *1 was bothered by it that he lied. (ii) *1 was bothered that he lied by it.

10.4. CONSTRAINTS ON GHOST ARC SPONSORS

429

Such sentences are impossible, given (43), since the dummy nominal i t would head a Cho arc, which would hence be a dummy arc. 15 The same principle explains why English (and other languages) has no verb permit­ ting both the extraposition dummy as a 2 , and a 3 which is also a 2 . Both of these are possible independently, but they do not combine. For example, one finds: (45) a. He pointed it out to me that Joe lied, b. H e t o l d m e J t o j o e l i e d ) ,

In (45a), the dummy nominal i t is a 2 and the original 2 , the complement, is also the head of a Cho arc. In (45b), the original 3 , me, is also a later 2 and the original 2s are also heads of Cho arcs. One might expect to find verbs permitting structures of the form (46a), e.g., like (46b, c): (46) a. Nom V Nom it Complement. b. *He told me it that Joe lied. c. *He showed me it that the substance was radioactive. But there is no such verb, as (43) predicts. For in a case like, e.g., (46b), it would have to be the head of a Cho arc:

Cho Cho/cg

me

showed

15 The same principle explains the nonexistence of passive versions of the example in (lb); repeated as (i):

430

10. GHOST ARCS AND DUMMY NOMINALS

There are other similar predictions from (43) with respect to the impossi­ bility of dummy chomeurs, all of which seem correct. Since (43) has as consequences all of (i)-(v) above, and these are im­ portant and apparently true results, not guaranteed by any independent principles as far as is known, one should seek to incorporate (43) in the theory. Our reason for thinking that as is (43) is too strong is that it is incompatible with the theory of nominal flagging touched on earlier in con­ nection with (26). In this view, flagging a nominal requires the arc of which it is the head to have a Marq arc successor. Adopting (43) as a PN law would imply that dummy arcs can never be flagged, surely an intolera­ ble consequence. Therefore, we are driven to the following less general formulation which incorporates as much of (43) as is consistent with the theory of flagging in Chapter 13: (48) PN Law 87 (The Dummy Arc Law) Dummy arc (A)

A

Not(Marq arc(A)) -> Nuclear Term arc (A) .

This thus allows Marq arcs as the single exception to the Nuclear Term arc character of dummy arcs. An obvious consequence of (48) is: (49)

THEOREM

Ghost(A)

λ

91 (The Ghost Arc Broad Sponsor Theorem) Sponsor (Β, A) -» Nuclear Term arc (B) ν Marq arc (B) .

Proof. Let A' be a ghost and B' its sponsor. It follows from The Ghost Arc Law that there is some arc, call it C', which is an R-successor of A' and which is a facsimile of B'. C' is thus a dummy arc, and hence, via The Dummy Arc Law, a Nuclear Term arc if not a Marq arc. Since C' is a facsimile of B', the latter is a Nuclear Term arc if not a Marq arc. QED. We would like to prove a stronger result than (49), namely that all ghost arc sponsors are Nuclear Term arcs: 16 (i) It frightens me the things he does. (ii) a. *1 am frightened by it the things he does. b. *1 am frightened the things he does by it. ^^(50) would almost follow from (27) since the latter entails that a ghost spon­ sor is a Term arc.

10.4. CONSTRAINTS ON GHOST ARC SPONSORS

431

(50) THEOREM 92 (The Ghost Arc Sponsor Theorem) Ghost(A)

Λ

Sponsor (Β, A) -> Nuclear Term arc (B) .

However, the proof of this depends on showing that a ghost arc cannot have an R-successor which is a facsimile of a Marq arc. This in turn de­ pends on assumptions only formalized in Chapter 13, so we delay the proof of (50) to the appendix of that chapter. As it stands, PN law 87 is slightly suspicious with its ad hoc refer­ ence to Marq arcs. Given that all Marq arcs are pioneers, as shown in Chapter 13, we could state PN law 87 more generally in terms of this con­ cept. It is even possible that ultimately one might replace the second conjunct of the antecedent of the current formulation simply by "Not (Immi­ grant (A))," counting on other laws to guarantee that certain dummy arcs are both immigrants and Nuclear Term arcs. We cannot investigate here these possibilities for a more elegant version of PN law 87. Another important principle worth stating is: (51) THEOREM 93 (The Marq Arc Status Theorem) Marq arc (A) -» Immigrant(A) . Again, however, the proof must be delayed until the appendix of Chapter 13. Given (51) and The Dummy Arc Law, one can then make good on the prom­ ise to show that every dummy arc head is a nominal: (52) THEOREM 94 (The Ghost Arc Head Label Theorem) Ghost(A) -> Head Label(Nom, A) . But since the proof of (52) depends on (51), we delay giving it until the appendix of Chapter 13. Finally, it follows from (52) and the definition of Dummy arc that: (53) THEOREM 95 (The Dummy Arc Head Label Theorem) Dummy arc (A)

Head Label (Nom, A) .

But for the reasons already given, proof is delayed until Chapter 13.

432

10. GHOST ARCS AND DUMMY NOMINALS

Given proofs of (50-53), it will be guaranteed that all dummies are dummy nominals and that ghost arcs give rise only to entities of this type. Assume that Theorem 92 has been proved. In principle then only four basic types of ghost situations are allowed: (54) a. a 1 arc sponsors a 1 arc ghost . b. a 1 arc sponsors a 2 arc ghost . c. a 2 arc sponsors a 2 arc ghost . d. a 2 arc sponsors a 1 arc ghost. Moreover, if, as assumed, ghosts can have either local or foreign sponsors, these four would subdivide into a total of eight types. However, the attested cases of ghost arcs seem to be a proper subset of these so far allowed possibilities. Restricting attention to local spon­ sorship cases, we know of instances of (54a), e.g., (15), (54b), e.g., (22), and (54c), e.g., where "extraposition" is found with an object, as in: (55) He mentioned it to me that the nurses were attentive. However, we know of no cases exemplifying (54d). Conceivably, one should impose a constrant of the form: (56) Ghost(B)

A

Sponsor (A, B) -» Not (Outrank (B, A)) .

Unrestricted to local sponsors, (56) allows the same ternary subset of the four possibilities in (54) for foreign ghost sponsors as for local ones. How­ ever, (56) is perhaps premature even for locally sponsored ghosts. And, in the case of foreign sponsored ghosts, as already indicated, the informa­ tion available is so limited as to make conclusions at this point very difficult. The extremely tight account of ghost arc sponsorship represented in (54) is even further restricted, by The Ghost Sponsor Organicity Law, which eliminates as possible sponsors those Nuclear Term arcs which are grafts. Moreover, the examples considered in this chapter are consistent with a still tighter limitation on ghost arc sponsors. This would require

10.4. CONSTRAINTS ON GHOST ARC SPONSORS

433

these to be domestic arcs, for we have given no cases where an immigrant arc sponsors a ghost. Conceivably, there are no such cases, and PN law 86 might be replaced by a stronger condition mentioning domesticity in­ stead of organicity. Actually, a still stronger condition may be possible, one limiting ghost arc sponsors to self-sponsoring arcs. However, there are facts in French, discussed by Ruwet (1975) in a transformational frame­ work, which seem to lend themselves to an APG treatment only if ghost arcs are permitted immigrant arc sponsors, hence nondomestic and neces­ sarily nonself-sponsoring sponsors. 17 Space precludes a serious discus­ sion of these cases here. But at the moment, PN law 86 seems the strongest constraint which can be safely imposed along these parameters. An obvious implication of our assumptions about ghost arcs is that no ghost arc can occur in a sentence not containing a nominal distinct from the head of that ghost arc. Since ghost arcs are not self-sponsoring, this is, also implied by PN law 43, The Self-Sponsoring Nuclear Term Arc Law. In the case of locally sponsored ghost arcs, our assumptions require there to be some other nominal besides the dummy in the same clause. There are various clauses containing dummies not obviously consis­ tent with these assumptions, clauses in which there are no surface nominals other than the dummy and no possibility of adding another nominal leaving the logical structure intact. Some examples: (57) a. It is raining. b. It is late. c. It is foggy. The current theory then requires analyses of such examples involving selfsponsoring Nuclear Term arcs which are erased and hence do not yield 17 Ruwet (1975: 116-21) shows, in transformational terms, that dummies are not subject to raising. And yet the extraposition dummy occurs in raised positions. Ruwet concludes that extraposition introduces the dummy by operating on the com­ plement clause which underwent raising. In our terms, this would mean that the immigrant arc involved in raising is the sponsor of the ghost arc of which the dummy is head. Hence the ghost sponsor could not be a self-sponsoring arc.

434

10. GHOST ARCS AND DUMMY NOMXNALS

surface arcs. In this respect, our account of ghost arcs and their sponsors simply makes more concrete what is already implied by The SelfSponsoring Nuclear Term Arc Law. While we are not prepared to provide detailed analyses for cases like (57), we forsee no difficulty in principle in treating such examples con­ sistently with our assumptions. For instance, it seems reasonable to treat cases like (57a) as involving a logical structure in which a predicate "fall" is associated with a nominal whose content is "rain." The sur­ face verb in (57a) would then involve incorporation of the rain nominal. Assuming that predicates meaning "fall" occur in initially unaccusative structures, this would lead to a partial analysis for (57a) along the lines of (58), assuming that the ghost arc is a 2 arc:18 (58)

FALL rain

Here B is the ghost arc sponsored by the self-sponsoring Nuclear Term arc C, which it overruns, yielding a Cho arc. The essential aspect of (58) for present purposes is that the nominal involving the noun stem rain, which would otherwise be visible, does not show up in the S-graph. This is so because all the arcs having the relevant nominal node (55) as 18

There is an alternative analysis in which the ghost arc would be sponsored by a 1 arc successor of the initial 2 arc. We hope to find grounds to exclude one of these in principle.

10.4. CONSTRAINTS ON GHOST ARC SPONSORS

435

head (and their branches) are erased, e.g., C, D, G, etc. (the erasure of the latter not indicated). However, as a function of the incorporation (tentatively indicated by the pair Sponsor(DjH)), the stem rain shows up as part of the verb. Structures such as (58) claim that a verb like English rain corresponds to the head of a P arc like E, that is, a P arc whose

head R-governs a phonological node, rain, also R-governed by the head of a 2 arc. While structures like (58) raise many questions and involve many un­ solved problems, we see nothing in such cases to suggest any grounds for weakening The Self-Sponsoring Nuclear Term Law or The Ghost Arc Law and The Dummy Arc Law, which jointly require that ghost arcs be spon­ sored by Nuclear Term arcs, and thus that dummy nominals co-occur with nondummy nominals, regardless of whether the latter have surface realizations. The Dummy Arc Law entails that dummy arcs cannot have Cho arc successors (since these would be Cho dummy arcs). Recall that when an arc is overrun by a nonreplacer, there are three different ways it can re­ main consistent with The Chomeur Law: (59) a. by being locally assassinated (hence zeroed) by its overrunner. b. by being locally assassinated by some other employed arc. c. by having a Cho arc local assassin. However, in the case of dummy arcs overrun by nonreplacers, option (59c) is excluded by PN law 87. Let us inquire into option (59a). Is it possible for a dummy arc to be zeroed by a nonreplacer overrunner? We know of no cases of this type and do not believe they can exist. We would like, there­ fore, to prove that this is impossible. Given The Nominal Arc Zeroing Law, we can prove this if we can show that heads of dummy arcs cannot be members of Inexplicit, i.e., can­ not be labeled O or UN. A prerequisite is: (60) THEOREM 96 (The D-R-Successor Nonc1 Arc Theorem) D-R-Successor(A, B) -» N o t ( c j(A)) .

436

10. GHOST ARCS AND DUMMY NOMINALS

Proof. Let A' be the D-R-Successor of B'. There is then some arc,

call it C', of which A' is the successor. There are two cases to con­ sider, where A' is a local successor and where A' is a foreign succes­ sor. If A' is a local successor of C', The Local Successor Coordinate Law determines that the first coordinate index of A' is +1 of the last coordinate index of C', and hence is greater than 1. If A' is a foreign successor, it follows from The Immigrant Coordinate Law that the first coordinate index of A' is +1 of the first coordinate index of the local sponsor of A', and hence is greater than 1. QED. (61) THEOREM 97 (The Dummy Arc Head/Inexplicit Incompatibility Theorem Dummy arc(A) a Head{ a, A) -> a / Inexplicit . Proof. Let A' be a dummy arc and a' its head. And assume the con­

trary of the consequent. Hence: (i)

a'e Inexplicit.

By PN law 82, The Inexplicit Binder Arc Law, it follows that: (ii)

(3C) (Head (a', C) Λ Binder Arc (C)) .

Let C be the binder arc in question. By definition such arcs are selfsponsoring: (iii) Head (a', C') a Self-Sponsor(C') . Recall PN law 13: (iv) (The Graft Overlap Law) Graft (A) A D -Overlap(AjB)AStructural (A a B) -> R-Successor(B,A). Now, since a' is the head of C' and of A', (iv) requires that C' must be an R-successor of A' if A' and C' are both structural. This is the case. For dummy arcs are Nuclear Term arcs or Marq arcs by PN law 87, and binder arcs are structural by definition. Since A'^ C': (v)

D-R-Successor (C, A').

C' is a binder arc. Thus, it is by definition self-sponsoring, and hence from The Self-Sponsor Coordinate Law: (vi)

C 1 (C).

437

10.4. CONSTRAINTS ON GHOST ARC SPONSORS

But Theorem 96 shows that: (vii) NotCc 1 (O). Thus the contrary of the consequent of the theorem, (i), leads to the con­ tradiction (vi) and (vii). QED. Returning to (59a), we have in effect shown that a dummy arc overrun by an arc which it does not sponsor (i.e., a nonreplacer) cannot be zeroed by that arc: (62) THEOREM 98 (The Dummy Arc Overrunning Nonzeroing Theorem) Dummy Proof.

Arc(A) Λ Overrun(B,A) ^Not(Sponsor (A,B)) -»iVoi(Erase(B,A)).

Let A' be a dummy arc, B' an arc which overruns A' and which

is not sponsored by B'. Suppose the contrary of the theorem: (i)

Erase (B', A').

The Nominal Arc Zeroing Law, PN law 76, determines that: (ii) Head(A') e Inexplicit. But (ii) contradicts Theorem 97. QED. Therefore, both (59a, and 59c) are excluded as possibilities for a dummy arc overrun by a nonreplacer. This leaves only possibility (59b). We know of no cases where a dummy arc is overrun by a nonreplacer and erased by employed arc distinct from the overrunner. A hypothetical case of this sort would be: (63) a. Hypothetical Sentence: It was given Mary the bracelet by Tom. b.

it

the bracelet

Mary

(by) Tom

(was) given

10. GHOST ARCS AND DUMMY NOMINALS

438

Here B is a ghost arc overrun (at

C3)

by the local successor 2 arc, E.

B is erased by A , an employed arc, contradicting no previous con­ straints on dummy arcs. While we know of no cases like (63), it seems premature to rule them out. Hence, we content ourselves with having shown that of the three possibilities in (59), at most one remains for dummy arcs. Theorems 97 and 98 show for dummy arcs something stronger than we were able to show for arcs in general in Chapter 9. There we pointed out that we had not guaranteed for arbitrary arcs that their heads were not members of Inexplicit and hence that they were, as desired, not zeroable by nonreplacer overrunners. However, Theorem 97 does show this for dummy arcs. The result is generalizable to all grafts, for the proof makes use of no properties of dummy arcs beyond the fact that they are grafts.19 However, we will not take the space to prove the more general result here. 10.5. Cho arc types and a further characterization of Cho arcs Having sketched our treatment of ghost arcs, we can briefly make ex­ plicit a further aspect of any viable account of Cho arcs, a typology of (domestic) Cho arcs imposed by (i) the R-signs of their predecessors (and hence of their predecessors' overrunners) and (ii) the overrunning arc type along a dimension to be explicated, (i) permits exactly three types of domestic Cho arcs to be distinguished: (64) Domestic Cho arcs whose predecessors are: a. 1 arcs b. 2 arcs c. 3 arcs However, we also distinguish domestic Cho arcs according to the nature of the arcs which overrun their predecessors. Here there are also three types:

Actually, it also makes use of the fact that dummy arcs are structural arcs.

10.5. CHO ARC TYPES

439

(65) Cho arc predecessor overrunners which are: a. Local Successors b. Immigrant Arcs c. Ghost Arcs While we believe (65) represents all and only those arc types which can be Cho arc predecessor overrunners, we have not proved this. At issue is whether there are grafts distinct from ghost arcs which can "induce" Cho arcs. Only grafts are at issue, for (65a, b) exhaust the class of organic arcs except for self-sponsoring arcs. But self-sponsoring arcs cannot overrun any other arcs. Consequently, all Cho arc predecessor overrunners are provably of the types in (65) if the only grafts which can "induce" Cho arcs are ghosts. Before considering this problem directly, we note both the informality and clumsiness of the concept 'induce' of the previous paragraph. We can avoid this and make the discussion formal in a convenient way by taking account of the fact, guaranteed in Chapter 8, that domestic Cho arcs are cosponsored by a predecessor and an overrunner of that predecessor. What we need is a convenient way of referring to the sponsorship of a domestic Cho arc by its predecessor's overrunner. We can achieve this by defining a Sponsor relation subtype in which the related arcs do not overlap: (66) Def. 160: Spawns(A l B) «-> Sponsor (A,B) ANot (Overlap (A,B)) . Hence, Spawns bears the same relation to Sponsor as Zeroes does to Erase. Observe that while a domestic Cho arc is sponsored by both its predecessor and its predecessor's overrunner, it is only spawned by the overrunner. (65) is then a typology of the kinds of arcs which can spawn domestic Cho arcs. And we would like to prove that (65) provides an ex­ haustive typology of domestic Cho arc spawners. To do this, as already noted, we must guarantee that no nonghost arc grafts can spawn domestic Cho arcs. We can accomplish this and also account for the fact that, to our knowledge, there are no Nominal arc grafts which are not ghosts or replacers by imposing:

440

10. GHOST ARCS AND DUMMY NOMINALS

(67) PN Law 88 (The Nominal Arc Graft Law) Nominal Arc (A) Λ Graft(A) Λ Not (Ghost (A)) -» (3B) (Replace (A,B)) . Therefore: (68) THEOREM 99 (The Domestic Cho Arc Graft Spawner Theorem) Cho arc(A) ADomestic(A) ASpawn(B l A) AGraft(B) -> GZiosf(B) . Proof. Let A', whose predecessor is C', be a domestic Cho arc

spawned by a graft B'. We then know from The Cho Arc Second Sponsor Identity Law that: (i)

Overrun (B', C').

Hence, from the definition of "Overrun": (ii)

Term x arc(B'aC') .

Suppose the consequent is false. Therefore: (iii) Not (Ghost (B')). Since B' is a Term arc, it is a Nominal arc. Therefore, B' being a graft, we conclude from (iii) and The Nominal Arc Graft Law that there is some arc which B' replaces. Call this D'. Hence: (iv)

Replace (B', D').

It then follows from the definition of "Replace" and the fact that B' is a Term x arc that: (v)

Term x arc (D').

Suppose without loss of generality that: (vi) (D'). Then The Replacer Coordinate Law determines that: (vii) (B'). Now, since (i), we can conclude: (viii) (C')· For otherwise The Stratal Uniqueness Theorem would be violated by B' and C'. Since (vi) holds, The Stratal Uniqueness Theorem is contradicted by C' and D', unless these are the same arc. Therefore: (ix) C'= D'.

10.5. CHO ARC TYPES

441

But Theorem 66, The Cho Arc Predecessor Local Assassination Theorem, entails that: (X)

Erase (A', C').

And The Replacer Erase Law and (iv) entail that: (xi) Erase (B', D'). The conjunction of (x) and (xi) contradicts The Unique Eraser Law, unless A' = B'. Therefore: (xii) A'=B'. However, (xii) is a contradiction, since A' is a Cho arc and B' a Term arc. QED. Thus, all possible domestic Cho arc spawner types are listed in (65) (or rather, this follows from the proof that self-sponsoring arcs cannot be spawners of Cho arcs, which in turn follows from The Chomeur Law, given the trivial point that all such arcs have C1 for their first coordinate, pre­ cluding them from overrunning any other arcs). All those Cho arcs which are not domestic are now strictly characterized: (69)

THEOREM

100 (The Graft Cho Arc Theorem)

Cftoarc(A)AGrafi(A) -» (3B)(flep/ace(A, B)) . Proof. Let A' be a Cho arc graft. It follows from The Dummy Arc Law

that A' is not a ghost arc. Therefore, since Cho arcs are Nominal arcs, PN law 88, The Nominal Arc Graft Law, determines that there is some arc which A' replaces. QED. 20 Given earlier proofs that Cho arcs cannot be self-sponsoring arcs (Theorem 62) or immigrant arcs (Theorem 61), it follows that:

20The considerations underlying the proof of Theorem 100 also permit proofs that: (i) (ii) (iii)

Oblique arc(A)\ Λ Graft (A) -» (3B) (Replace (A,B)) Dead arc(A) > 3 arc(A) j

We leave these as an exercise for the reader.

442

10. CMOST ARCS AND DUMMY NOMINALS

(70) THEOREM 101 (The Cho Arc Characterization Theorem) Cho arc (A) ->((3B) {Local Successor (A,B)))

Not ((3C) (Replace (A ,C))).

Proof. Let A' be a Cho arc. Theorems 61 and 62 require that if A' is organic, it is a local successor. It follows from Theorem 100 that if A' is not organic, it is a replacer. QED. Return to domestic Cho arcs (to Cho arc local successors of Term arcs). The following compressed definitions yield a ternary subdivision of such Cho arcs: (71) a. Def. 161

'Advancement

b. Def. 162

Immigrant

c. Def. 163

Ghost

(-Induced) Cho arc(A) «-> (3B)(3C) Domestic

(Local Successor (A,B) ASpawns (C, Α) Λ Immigrant

(C)) .

Ghost The right-hand side of (71) need not specify that an arc instantiating the variable A is a Cho arc because this is provable from the fact that it has both a local predecessor and a spawner, and is hence a cosponsored domestic arc. The right-hand side need not specify that C overruns B, for analogous reasons. On the same basis, it is also sufficient to say "Domestic" on the right-hand side, since self-sponsoring arcs cannot be spawners of domestic Cho arcs. Parallel to earlier definitions, we could characterize the nodes which are heads of the three arc types defined by (71) as advancement-induced chomeurs, immigrant-induced chomeurs, and ghost-induced chomeurs, But we will not bother with this here. However, the three types of chomeur are respectively exemplified by the italicized nominals in: (72) a. The turkey was caressed by the minister. b. I believe Ted to sing. c. It frightens me the things they are planning.

10.3. CHO ARC TYPES

443

Extratheoretically, we can observe that it is typical for advancementinduced chomeurs like that in (72a) to have a special flagging, while this is rare for immigrant-induced chomeurs and possibly unheard of for ghostinduced chomeurs. A priori, the typology of Cho arcs imposed by (71) ihould croSsclassify w'ith that implicit in (64), which we now make explicit:

(73) Def. 164: Term x (arc-lnduced)Cho arc(A) •-» Cho arc(A) A (3B)(R-Local Spawns (B,A) ATermx arc(B)) , The tricky part of (73) is its use of the ancestral of Local Spawns. The motivation is to define as, e.g., 3 arc Induced Cho arcs, not only those domestic Cho arcs spawned by 3 arcs, but also those replacer Cho arcs which replace Cho arcs spawned by 3 arcs. Both these Cho arc types are R-Local Spawned by Termx arcs, and the formulation in (73), as opposed to one making use of R-Local Sponsor, guarantees that each Cho arc is of a single Termx arc induced type. That is, in a replacer Cho arc case like: (74)

α

b

we want both D and E to be 2 arc Induced Cho arcs. (73) guarantees this since both are R-Local Spawned by the 2 arc A. Moreover, although the 3 arc B R-Local Sponsors both D and E, it does not R-Local Spawn either of them, guaranteeing properly that neither D nor its re­ placer E is a 3 arc Induced Cho arc. Thus definition (73), like definition (71), makes use of the fact that domestic Cho arcs are sponsored (spawned) by the overrunners of their predecessors. Again, as in the case of the typology in (71), it is possible to extend that in (73) to characterize the

444

10. GHOST ARCS AND DUMMY NOMINALS

nodes which are the heads of the types of arcs defined. This is straight­ forward, and we abstain from giving the definitions here. The typology of Cho arcs in (71) depends on the nature of the Cho arc spawner along the dimension Local Successor/Immigrant/Ghost, while that in (73) depends on the R-sign of a Cho arc R-spawner. A priori, these two independent classifications would intersect freely, defining nine logically possible types of Cho arc. However, there is evidently a gap. Ghost-induced Cho arcs require ghost overrunners for their predeces­ sors. But The Dummy Arc Law precludes the possibility of there being 3 arc ghosts. Consequently, there can be no 3 arc Induced Cho arcs which are Ghost-Induced Cho arcs. Hence, at most, eight of the nine types of domestic Cho arcs can exist, given current assumptions. We believe that all of these eight do exist, although it is not so easy to find 3 arc Induced Cho arcs which are Immigrant-Induced Cho arcs. 21 Our motivation for defining these Cho arc types is the assumption that the grammars of individual languages are sensitive to the categories de­ fined. For instance, we assume that in English the flagging of passive chomeurs with by is actually the function of a rule sensitive to the notion of 1 arc Induced Cho arcs which are Advancement-Induced Cho arcs. Thus, if, following note 21, APG theory makes available the concept 1 A Cho arc, it will be the heads of such arcs whose flags have the form by in English. 10.6. Further properties of dummy rtominals It was noted at the beginning of this chapter that the form of visible dummy nominals in a given language corresponds to the form of one or another definite anaphoric pronoun in that language. One can probably go

21 The terminology here is hopelessly clumsy. One should introduce ways of combining the types given by (71) and (73) to talk about, e.g., 1 arc Induced Advancement-Induced Cho arcs, etc. These could be effectively abbreviated by taking the first letters of "Advancement," "Immigrant," and "Ghost," and leaving out "arc" and "Induced," to yield notations like:

10.6. FURTHER PROPERTIES OF DUMMY NOMINALS

445

further and specify that the form is that of singular definite anaphoric pronounds, for we know of no cases of dual, plural, etc., dummy nominals. Although these observations are relatively standard by this time, no lin­ guistic theory has given any principled basis for this. At issue is why, e.g., in English, the visible dummy nominals, namely, it and there, are identical in form to anaphoric pronouns, e.g., those itali­

cized in: (75) a. Melvin picked up the meatball and took a bite out of it. b. Melvin visited Des Moines but I wouldn't go there on a bet. One would like principles which guarantee that dummy nominals are drawn from the class of forms independently serving as anaphoric nominals. Such principles would claim, consistent with everything known about dummy nominals, that forms like the following are not possibly dummy nominals in any language: (76) a. Melvin

f. peaches and cream

b. the girl on the corner

g· few gorillas

c. the claim that God exists

h. Nim Chimpsky's trainer

d. Your caressing the beaver

i. that dinosaur liver

e. For real love to exist

j· such garbage

One can ask whether our reconstruction of dummy nominal in terms of the notion Head of Ghost Arc makes any contribution to yielding this range of predictions. The answer seems to be that it makes a little, but not nearly enough. The impossibility for forms like those in (76) to function as dummy nominals is, we suggest, connected to the following observations. Forms

(i)

1 A Cho arc (i. e., a Cho arc spawned by a a 1 arc which is a local successor) (ii) 2 I Cho arc (iii) 1 G Cho arc (iv) 3 I Cho arc

446

10. GHOST ARCS ANP DUMMY NOMINALS

like those in (76) have meanings, 22 while, as is part of general grammati­ cal lore: (77) Dummy nominals have no meaning, Phrases like "have (no) meanings" are quite imprecise. However, in our terms, to say that some constituent corresponding to a nonterminal node η f

*has meaning" can only be true if η is node-extractable from an L-graph,

thgit is, if η is the endpoint of a logical arc. Therefore, one could con­ tribute to explicating the assumed truth (77) by proving that: (78) Dummy (a) λ L-graph (X) -» Not(Node-Extractable(a, X)) . It might seem trivial to prpve (74), but it is not and we have not done so. It seems easy at first for the following reasons. Since ghost arcs are grafts, they are not themselves possible members of L-graphs, so their heads cannot be node extractable from L-graphs without being the endpoints of some nonghost arcs. However, PN law 13, The Graft Overlap Law, precludes the possibility that any self-sponsoring structural arc can overlap a structural graft. Thug, it is easy to prove that dummy nodes are not the heads of any logical arcs. To prove (78) then, it suffices to show that dummy nodes cannot be the tails of any logical arcs. But although this can probably be done, we have not accomplished this so far, and (78) remains a conjectured theorem. Suppose (78) were proved. We would then have a reasonable basis for the "meaninglessness" of dummy nominals, i.e., for the fact that such nominals make no contribution to the logical structures of sentences. This would be an important result. By itself though, it would still not explain the impossibility for forms like those in (76) to serve as dummy nominals. Evidently, an explanation of this must somehow depend on the fact that

22

Except, e.g., in the case of the proper name Afeivin, where it is not custom­ ary (or, we think, reasonable) to posit any meaning. Nonetheless, such forms will, as noted in Chapter 4, have L-graph representations in APG terms, representations to distinguish logically Melvin from, e.g., Ted.

10.6. FURTHER PROPERTIES OF DUMMY NOMINALS

447

forms like those in (76) can only occur with "meanings." This is a prob­ lem about which we have no insight. The point is not that, e.g., peaches and cream, can only occur in English with some meaning, but that in prin­

ciple languages cannot have such forms with no meaning, a deeper matter. Finally, even if We were able to prove (78) and even if we understood why forms like (76) cannot be meaningless, this would not explain the re­ lationship between the form of dummy nominals and anaphoric pronouns. We believe that some insight into this matter is derivable from the study of anaphora. In Chapter 11 we provide a definition of the notion Pronomi­ nal Arc, which is a subtype of Nominal arc covering those arcs relevant

for anaphoric phenomena. It turns out that ghost arcs are subsumed under this concept. Hence, a partial basis for the similarity in question is available. But a great deal remains unaccounted for even in these terms. For instance, conjoined anaphors are quite possible, as (79a) shows, but we know of no language with dummy nominals of the form in (79b): (79) a. Joe told Mary that he and she should not be seen together, b. he and she In general then, while some light is thrown on the questions raised in this section by the APG framework, much remains mysterious. A great deal more work is necessary before anything like a full-fledged theory of dummy nominals is available.

CHAPTER 11 REPLACERS AND ANAPHORA 11.1. Basics

In this chapter, we sketch how the concept Replace contributes to solving various problems raised by a conception of "coreference" as in­ volving overlapping self-sponsoring Nominal arcs. We develop the outlines of a theory of pronominal anaphora and show how it deals with certain issues in the domain of anaphoric connections. One result is that although there is clearly a "grammatical relation" representing anaphoric connec­ tions between elements, it is unnecessary in the APG framework to recog­ nize a primitive to represent this relation. This is so because it is possible to provide an effective definition of the anaphoric relation in terms of the basic APG notions Sponsor and Erase. As touched on at numerous points, one basic insight easily incorporable in a relational approach to grammar1 is that there is no such thing as a primitive relation of "coreference" in the sense assumed in grammatical discussions over the last decade.2 Rather, we take, e.g., examples like (la) to involve a single nominal node, that corresponding to Mary, occur­ ring as the head of two distinct self-sponsoring arcs: (1) a. Mary praised herself. b. Mary praised Joe. c. Joe praised Mary.

1 But 2 See

not new to it, see section 5 below.

in particular Postal (1970), Partee (1972), Lakoff (1968), Jackendoff (1972), Wasow(1972), Jacobson (1977), and McCawley (1973).

449

11.1. BASICS

The pronominal element, here herself, is normally said to be "{preferen­ tial" to its "antecedent." But, in APG terms, herself plays no logical role, is not part of an arc included in the L-graph. The analysis of examples like (la) which takes the nominal node corresponding to Mary to be head of two self-sponsoring arcs seems abso­ lutely perfect from a logical point of view. For this claims precisely that the relevant node plays both of the roles together in (la) which its corre­ spondents play separately in (lb) and (lc). And this is evidently absolute­ ly correct. Thus, we reconstruct in this way traditional statements which say things about sentences like (la) of the form: "the same element is subject and object of the verb." Although we deny that elements like herself in (la) play any role logi­ cally or have any semantic connection to their "antecedents," there is, nonetheless, an obvious relation between, e.g., Mary and herself, in such cases. Let us call it, vaguely and imprecisely for the moment, an ana­ phoric relation. Our aim is to see how the concept Replace permits an explication of anaphoric connections of this type. The essential idea, implicit in many earlier analyses, is this. Socalled "coreferential anaphora" between nominals in cases like (1) is actually a case of cosponsoring of a replacer graft by two self-sponsoring arcs. 3 In (la), herself corresponds to the head of a replacer whose two sponsors are the 1 arc and the 2 arc headed by the node corresponding to Mary. The basic analysis of (1) is thus: (2)

Mary herself

praised

3This characterization does not cover equi cases, which do not involve replacers in our terms. See (161) below for an example of how this is described.

450

11. REPLACERS AND ANAPHORA

Here C is a cosponsored graft which meets the conditions of Replace. Thus, the first coordinate of C is determined from the last coordinate of B by The Replacer Coordinate Law, and the fact that C erases B (zeroes it) is determined by The Replacer Erase Law. A number of interesting questions arise about structures like (2), some of which interact with questions about APG rules. In particular, what determines that it is the 2 arc which has a replacer and not the 1 arc, and what determines that there is a replacer at all, e.g., what pre­ cludes overall PNs of the form: (3)

Mary

praised

Such structures would yield sentences of the form: (4) *Mary praised. with the same meanings as (la). We consider structures like (3) impossi­ ble and, more generally, claim that no structural arc in an S-graph can overlap any other structural arc. The reason is, basically, PN law 94, discussed in section 9 below. This greatly limits the distribution of dis­ tinct overlapping structural arcs "internal" to constituents. This law re­ quires all but one of a set of overlapping self-sponsoring structural arcs to be erased and, moreover, erased in a certain way. The existence of replacer structures like that in (2) is one major way in which PNs can re­ main consistent with this PN law. Another is for one of a set of distinct overlapping self-sponsoring arcs to erase others. While this is possible in general, it is precluded in cases like (3) by PN law 11, The Parallel Assassin Law. Hence, for this subclass of cases, the replacer alternative is crucial. We return to these questions below.

11.1. BASICS

451

Significantly, the apparatus of anaphoric connection which functions in cases of so-called "coreference" also invariably functions in parallel ways in so-called "copy pronoun" cases. Thus, alongside the "coreferential" anaphora in (5a) one finds the "copy" anaphora in (5b): (5) a. Joe says he is dying. b. Joe looks like he is dying. (5b) is not a case of "coreference" but of raising,4 as indicated by the possibility of dummies in this construction: (6) There looks like there is going to be a riot. It is thus a raising construction in which a "copy" is "left behind." The properties of "copy" anaphora and "coreferential" anaphora seem normally to go together. Both types obey the same general conditions, e.g. (7) a. *He says Joe is dying. b. *He looks like Joe is dying. We conclude that the notion 'anaphoric connection' links pairs of nominals like Joe/he in both (5a, b). In APG terms, the two cases are as follows. Both involve replacers sponsored by overlapping structural arcs. But in "coreferential" anaphora, the two arcs are self-sponsoring, while in "copy" anaphora, the two arcs are predecessor and successor. In (5b), it is the immigrant arc involved in the raising and its downstairs predecessor that are the two sponsors of the 1 arc replacer whose head corresponds to he.

A key task for linguistic theory is then to define a notion of anaphoric connection which holds indifferently in both "coreferential" and "copy" cases. This notion will correctly indicate that the same relation holds

^This is shown further by such contrasts as: (i) a. It says Joe is dying. b. It looks like Joe is dying. (ib) is interpreted with it as a dummy, but this is impossible for (ia).

452

11. REPLACERS AND ANAPHORA

between Joe and he in both (5a, b), this in spite of the important structural differences between the two PNs. We will accomplish this by defining a relation ^rc Antecedes, which holds between an arc A and an anaphoric arc B . The definition is designed in such a way that, with respect to, e.g., (2), A arc antecedes C. Thisisrathertrivialsincethereisonly a single anaphoric arc in (2). But in more complicated cases the result is far from trivial. Let us consider cases like (8a, b) and the French clause in (8c). (8) a. Each one of us wants to tickle himself (*ourselves). b. We each want to tickle ourselves (*himself). c. Les femmes, pa croit que pa a des droits. the women that thinks that that has of the rights = "Women, they think that they have rights." Consider the latter first. The key property of such examples is that the left dislocation construction requires a copy pronoun. Subject to rules which need not concern us, the copy need not agree fully with its "ante­ cedent." However, internal to the clause, other pronominals anaphoric to the left dislocated nominal must agree with the copy. One cannot replace the second pa in (8c) by elles (= they, feminine). In (8a, b) the key issue is why so-called "quantifier floating" (see Postal [1976]) in the main clause effects agreement in the subordinate clause. We would deal with these issues initially by providing (8b, c) with, respectively, the PNs in (9) and (10):

453

11.1. BASICS

(9)

want

'.::.- - - - - - 1 - c, GR x ourselves each one

200

GR'\ us

(10)

Top

®

I c2

® ®

©

a

2

®

les femmes

yo

9°

clc2 des droits

454

11. REPLACERS AND ANAPHORA \

(9) is a case of "coreferential" anaphora. G is a "coreferential" arc (see below), present because of the overlapping arcs B and C , which share node 100 as head, and determine the replacer G . This node is also the head of A. "Quantifier floating" is, in effect, the existence of the immigrant arc M, successor of K. We want to define "anaphoric con­ nection" in such a way that the head of G is anaphorically connected to node 100. This would normally lead to it being third person singular, as in (8a). It is, however, an ad hoc fact that node 100, which is third person singular in cases like (8a), must have the agreement properties of node 200 (here first person plural) when arc M exists. Hence the establishment of an anaphoric connection between the head of G and node 100, needed for the general case, including those like (8a), will suffice to establish indirectly a connection between G's head and node 200. We want to do this by defining a notion of arc antecedence holding between arc B and G. This will combine with the ad hoc agreement relation between nodes 100 and 200 to guarantee that the head of G ends up agreeing with us. The possibility of an analysis like that just hinted at depends totally on the fact that in an APG analysis of equi constructions like (9) the same node (here 100) is head of an upstairs arc (relevantly, A) and a downstairs arc (relevantly, B). Thus, properties of A and its head are automatically properties of the head of B. This is why "quantifier floating" upstairs has the power to effect downstairs agreement. In (10), both C and G are anaphoric arcs. G is a "coreferential" arc present because Ies femmes is the head of the self-sponsoring 1 arcs of both the croit clause and the a clause. C is a "copy" arc, needed as a function of the fact that the left dislocation construction requires copies. Again, our goal is to define "arc antecedence" in such a way that C arc antecedes G in (10). This will permit a simple account of the fact that the head of G is third person singular, even though the (identical) heads of G's cosponsors are third person plural. In both (9) and (10), the assumed underlying principle governing agreement between an anaphoric pronoun and its antecedent is that such a pronoun agrees with the nominal

11.1. BASICS

455

corresponding to the head of the arc which arc antecedes the arc of which it is the head. We develop this idea further below. The odd thing about examples like (8c) is that under certain conditions the head of an arc anteceded by a Top arc need not agree in the ordinary way with the head of its anteceding arc. Under these conditions, pairs like Ies femmes/pa are proper "agreement" pairs, although the former is plural and the latter singular. This, however, is an idiosyncracy of French, and not of direct interest here. Just so, it is an idiosyncracy of English that in cases like (8b), as represented in (9), node 100, normally, third person singular, must have the properties of node 200. However, it is the existence of such idiosyncracies which reveals the importance of a notion of anaphoric connection like that of direct concern. For it is this notion which will insure that, e.g., while, alongside (8c) one finds (11a), (lib) is not a related form: (11) a. Les femmes croient qu'elles ont des droits. the women

believe that they have of the rights =

"Women believe they have rights." b. Les femmes, pa

croit qu'elles ont des croits.

that believes That is, elles in (lib) cannot be understood as anaphorically connected to Les femmes. Comparable points are made by such English examples as (12), involv­ ing "coreferential" anaphora, and by "copy" anaphora cases like (13): (12) a. I want to buy that boat because it handles itself well in rough weather. b. I want to buy that boat because she handles herself well in rough weather. c. *1 want to buy that boat because it handles herself well in rough weather. d. *1 want to buy that boat because she handles itself well in rough weather.

456

11. REPLACERS AND ANAPHORA

(13) a. That boat looks like it handles well because of its extra phramus. b. That boat looks like she handles well because of her extra phramus. c. *That boat looks like it handles well because of her extra phramus. d. *That boat looks like she handles well because of its extra phramus. (12a) would have a PN fragment of the form: (14)

GRx

GRw

GRx because

that' boat want

GR

buy itself

handles in rough weather

Here D and E are anaphoric arcs, and a task for a theory of anaphora is to guarantee that the head of E agrees with the head of D (not with the head of A), for this will permit (12a, b) while blocking (12c, d). Again, there is no primitive APG relation between D and E . Thus arc antece­ dence must be specified in such a way that D arc antecedes E . 11.2. Arcantecedence We begin by defining a notion of Pro(nominal) Arc: (15) Def. 165: Pro(nominal) Arc(A) Graft(A)ANominal arc(A)

λ

Not ((ΉΒ) (Sponsor (Β, Α) Λ Branch (B, A))) . Thus, a pro arc is a Nominal arc graft not sponsored by one of its branches.

11.2. ARC ANTECEDENCE

457

The latter condition is designed, as we see later (Chapter 13), to distin­ guish pro arcs from closures, which are sponsored by their branches. This definition means that, e.g., C in (2), G in (9), C, G in (10), and D, E in (14) are pro arcs, as desired. It also has the consequence that all ghost arcs are pro arcs if one can show that ghost arcs are not sponsored by their branches. (See section 10 below.) This is desirable since, as observed in Chapter 10, dummy nominals, which correspond to the heads of ghost arcs, behave like anaphoric pronouns in a number of respects. Evidently, not all pronominal arcs are "anaphoric arcs," a concept we make precise, along with two related notions for convenience: (16) Def. 166: Anaphoric Arc (A) «-> Pro arc(A)A(3B)(3C) (Cosponsor(B,C,A)) . (17) Def. 167: Anaphoric Replacement(A r B) «-> Anaphoric arc (A) Λ Replace (A,Β) . (18) Def. 168: Pronominalize(A,B,C) ("A pronominalizes B and C") Anaphoric Replacement(A1B) ASponsor(C1A) . The notion Anaphoric Arc separates the class of pro arcs into the comple­ mentary sets of ghost arcs and anaphoric arcs. Definitions 167 and 168 simply make explicit the connections between an anaphoric arc and its cosponsors. Definition 166 in (16) does not specify that an anaphoric arc is a replacer. This is unnecessary because it is a consequence of PN law 88, The Nominal Arc Graft Law: (19) THEOREM 102 (The Anaphoric Arc Replacer Theorem) Anaphoric Arc(A) -> (ΉΒ) (Replace (A,B)) . Proof. Let A' be an anaphoric arc. It follows from the definition that A' is a pro arc, and hence a Nominal arc graft. A' cannot be a ghost arc, since it is cosponsored by definition. But PN law 88 specifies:

458

11. REPLACERS AND ANAPHORA

(i) Nominal Arc(A)AGraft(A) A Not (Ghost (A)) - (3B) (Replace (A1B)). Hence: (ii) (ΉΒ) (Replace (A',B). QED. It is extremely useful to have a term which uniquely picks out that sponsor of an anaphoric arc which is not the arc it replaces: (20) Def. 169: Seconds(A,B) *-* (3C)(Cosponsor(C,A,B)AReplace(B,C)). Thus, an anaphoric arc is cosponsored by the arc it replaces and its seconder. To see how these notions apply, and to set the stage for our definition of "Arc Antecedes", consider an example like (21), whose relevant PN fragment is (22). (22) represents (21) on the reading where it is the indi­ vidual referred to by Joe who is also tickler and tickled: (21) Joe says he tickles himself. (22)

tickles he

himself

In such a structure, D and E are both pro arcs, since they are Nominal arc grafts not sponsored by any of their branches. Moreover, they are anaphoric arcs, since they are cosponsored, and each replaces an arc, as

Π.2. ARC ANTECEDENCE

459

required by Theorem 102, Hence, E is an anaphoric replacement for C and D is an anaphoric replacement for B. Further, E pronominalizes B and C, while D pronominalizes A and B. It can be seen that, in general, if A is an anaphoric replacement of B, A bears the same role in the structure as B does. Now, as in earlier structures, our goal is that in (22), D arc antecede E. On the other hand, in (22) it is A which arc antecedes D. That is, in (22): (23) a. ArcAntecede(A l D). b. Arc Antecede (D, E). Arc antecedence is intransitive. We do not, e.g., want A to arc ante­ cede E. Hence, a formal definition must guarantee this in transitivity. Second, an example like (22) illustrates that there are two different types of cases involved in arc antecedence. In those like (23a), the relation holds between a nonanaphoric arc and an anaphoric arc, while in those like (23b) it holds between two anaphoric arcs. We can make this more precise, if we introduce the notion C lan, which is a maximal set of overlapping structural arcs. This is intended so that, e .g., A, B, and C in (22) will be all and only the members of some clan: (24) Def. 170: Let X = IAj 1 --^A n J be a nonnull set of arcs. Then: CIan(X) «-* (Vi, l Overlap (A,B).

For (57) entails that if A and B cosponsor an anaphoric arc, they are members of some clan. It seems, given examples like (56), that the strongest tenable analogue of (57) would require that the cosponsors of an anaphoric arc be members of a single Family, where Family is a notion ultimately defined such that all clans are families but not conversely. Given such a notion, one would propose as a PN law instead of (57) something like: (58) Cosponsor (A,B,C) λ Replace (C,B) - (3F)(Family (Χ λ A f X λ B e X). We cannot formulate even this weaker principle as a PN law at this point due t® the fact that "Family" has not been defined. Moreover, we cannot presently define the needed concept. Informally, it seems that in cases where the arcs in a family do not overlap, the conditions of membership involve some kind of similaritybetween the constituents with points cor­ responding to the heads of the arcs. Overlapping arcs then trivially meet

11.4. CONSTRAINTS

479

the similarity condition for family membership (i.e., it is trivial that all clans are families) since identical constituents are necessarily similar. Unfortunately, we have no insights to offer as to the nature of the simi­ larity condition in question10 and thus are left with the theoretical gap induced by our current inability to define "Family." It is nonetheless important to have isolated the point Where more needs to be said. There is a weakness (one of many obviously) in the present theory in that the possible cosponsors of anaphoric arcs are not strictly limited. However, the account of anaphora developed applies re­ gardless of the nature of these cosponsors, and thus it is correctly pre­ dicted that anaphora based on families which are not clans obeys the same conditions involving arc antecedence and anaphoric chains as that based on clans (although no doubt other, stricter conditions as well). Finally, while we cannot currently characterize generally the nature of all anaphoric arc cosponsors, we can provide much stricter constraints on these in cases where both sponsors are a member of a single clan. This question is taken up in section 6. 11.5. Forerunners and an objection As noted earlier, representing "coreference" through the multiple attachment of a single node, that is, in our terms, having a single node be the head of more than one arc, is not original here. The exact origins of this idea are obscure to us. But it has been around in one form or another since at least early in the previous decade. It is found in a rather vague form in stratificational writings, see particularly Hockett (1966: especially 278, 279). It is also suggested in Morin and O'Malley (1969:182), who remark:

10It might be worth starting with the view that the constituents which must be similar are isomorphic, that is, alphabetic variants differing only in the choice of nonterminal nodes. This is probably too strong a conditio», but perhaps some natural weakening can be found.

480

11. REPLA CERS AND ANAPHORA

Deleting axioms A2 and A3 generalizes the definition of a tree so as to permit more than one node to dominate a single node. Such a structure is a type of directed graph without cycles and will be called a vine. A vine is a set of nodes N with relations H and L such that L is a total order and H is a partial order. The following are three examples of vines: (19)

a

a

b

a

b

Vines offer certain economics in the representation of linguistic structures. In order to indicate multiple relationships such as being the subject or object of different verbs, it is necessary for a word or variable to appear on more than one node of a tree. Vines, however, can express multiple relationships by having many different nodes dominate a single word or variable. Vines may thus be used to eliminate multiple occurrences of a node within a tree. Conversely, variables may be used to represent vines as disconnected trees. The use of trees in semantic representation, rather than ele­ ments from some other class of formal objects, may well have been an historical accident. There is probably no theoretical reason to prefer trees with variables to vines; vines, however, are confusing and cannot always be drawn in two dimensions without crossing lines. More recently, a similar idea was proposed by Sampson (1975), and taken up by Saito (1976), who provided some empirical evidence for viewing "coreference" in such terms. A similar idea has also recently been adopted by Lakoff (see Lakoff [1977]). Related notions are also found in Hudson (1976: 76-79). It would not be unjust, however, to say that the multiattachment approach to "coreference" has never before been embedded within an articulate theoretical framework. In particular, there has never been any systematic account of how this basic idea interacts with the description of pronominalization and phenomena like equi constructions. The relevant contribution of the present theory then is to embed this idea in a coherent and articulated framework and to provide the basis for answers to these questions. The main virtue of our account of anaphoric connection based on the concept of replacers sponsored by members of a family (usually a clan) is

481

11.5. FORERUNNERS AND AN OBJECTION

that it yields an account of the interaction between the representation of "coreference" via multiattachment and the existence of pronouns which normally "represent" coreference. Thus, the APG approach provides the materials for rejecting the one criticism of the multiattachment idea known to us, that of McCawley (1968a), who directed his critique against the ver­ sion of this idea advanced by Hockett (1966). McCawley (1968a: 577-78) claimed: Loops 11 occur in Hockett's diagrams only in the case of coreferential noun phrases, as in The man shot himself, which Hockett diagrams as in Fig. 2. This structure has one advantage over that proposed as the deep structure of such sentences in Chomsky's Aspects, namely avoidance of redundantly repeating the lexical material of the man or the corresponding semantic material. A major defect which it shares with the proposals of Aspects is that it makes no provision for the fact that the intended reference of a con­ stituent has to be separated from the corresponding lexical material to account adequately for the meaning of such sentences as John denies that he kissed the girl who he kissed. This sentence is ambiguous, between a sense which asserts that John uttered a con­ tradiction such as "I deny that I kissed the girl who I kissed", and a sense which asserts that John denies having kissed a certain person, whom the speaker describes as "the girl who John kissed". Both senses involve some proposition X kissed Y in the comple­ ment of deny; they differ as to whether the identification of Y as the girl who X kissed is also part of the complement of deny. The only way I can see of adequately representing this difference is in terms of structures such as those of Fig. 3, in which the lexical material of noun phrases is separate from the corresponding "refer­ ential indices". A similar analysis is needed for Peter Geach's sentence Sir John Carstairs seduced his widow's sister two weeks before he married his widow, which is bizarre if his widow is taken as semantically within the scope

NP:x

NP:x

NP:x

X^y denies S John the girl who Xjy kissed

Xjy denies S

Xjy kissedX^g

FIGURE 3a

John NP:x

Xjy kissed x^g the girl who Xjy kissed FIGURE 3b

11

McCawley's use of "loop" here is distinct from ours. loop seems to correspond to our notion Cycle (see (4.16c)).

His conception of

482

11. REPLACERS AND ANAPHORA

of the past tense morpheme, but not if it is taken as outside its scope (i.e., as referring to the woman who is NOW his widow). If Hockett's diagrams were modified in this direction, the only reason ever advanced for having "networks" rather than trees for "sememic" representations would vanish: diagrams such as those of Fig. 3 already indicate coreferentiality without redundant duplica­ tion of lexical or semantic material. Moreover, multiple tokens of referential indices would make unnecessary the rule which Hockett would otherwise need, which would disconnect all his multiple con­ nections and attach pronouns at the loose ends. It is highly unliker Iy that such a rule could be stated, since whether a pronoun can refer to a given noun phrase depends not on the semantic structure of the sentence, bat on the structure which results after applying a large number of transformations (Ross 1967a). (Italics ours: D.E.J./ P.M.P.) McCawley's criticisms seem off the mark. Structures with multiple occurrences of the "same" referential index need not, it is true, necessari­ ly involve repetition of redundant lexical material. But they do, by defini­ tion, involve repetition of indices, and, as the possibility of overlapping arcs shows, this is redundant.12 This leaves a criticism about the neces­ sity of a rule to "disconnect" multiple connections and attach pronouns, which McCawley doubted the possibility of stating. The idea that such a rule is otiose is mistaken. For any theory must provide principles to gen­ erate pronouns and their anaphoric connections. In the APG framework, what is needed is the possibility for pairs of overlapping self-sponsoring arcs (restricting attention again to clans) to cosponsor anaphoric arc replacers, setting up the mechanisms which define anaphoric chains via completely universal apparatus. Such a possibility for replacer cosponsorship can also be regarded as universal (leaving vari­ able "pronominalization constraints" to language-particular rules). We conclude that McCawley's criticisms of "multiattachment" and advocacy of multiple occurrences of the "same" variable do not go through, at least interpreted as applied to the APG framework (which is an unfair interpreta­ tion, in the sense that McCawley was criticizing something quite different). 12 The fact that repeated occurrences of indices have an historical priority in both logical and linguistic work is no argument for them as against multiple attach­ ment of single indices (nonterminal nodes).

483

11.5. FORERUNNERS AND AN OBJECTION

A final point. Given that two overlapping arcs do cosponsor a replacer for one, the fact that, in McCawley's terms, one of the arcs is "disconnect­ ed" is a consequence, in APG terms, of an extremely general law, The Replacer Erase Law. We see below, moreover, that the erasure in question for overlapping self-sponsoring arcs which sponsor replacers is identical, works by the same mechanisms, as the independently needed erasure for "copy" pronoun cases, which involve overlapping arcs of a different sort. In APG terms, the "disconnection" of overlapping arcs which represent "coreference" is accomplished by the independently needed mechanism relevant for "copy" pronouns.

11.6. Two types of anaphoric connection We have remarked that there are two types of anaphora based on clans, "copy" anaphora and "coreferential" anaphora. We wish to build these informal remarks into the formal theory, and to elaborate these concepts and state various restrictive laws about the two types. To facilitate this, further definitions are necessary. These divide the class of anaphoric arcs into a number of subtypes, permitting immediate definition of the anaphoric node types corresponding to the heads of such arcs. We begin by formally picking out the domain of anaphoric arcs whose sponsors are members of families which are clans: (59) Def. 176: Kernel Anaphoric Arc(A) Pronominalize (A,B,C)

Λ

Overlap (B,C). Thus, kernel anaphoric arcs are anaphoric arcs which pronominalize pairs of overlapping arcs. (60) Def. 177: Copy Arc(A) «-» (3B) (3C) (Anaphoric Replacement(A1B)A Successor (C,B)). (61) Def. 178: Inherent Anaphoric Arc(A) AnaphoricArc(A)A Not (Copy Arc(A)).

484

11. REPLACERS AND ANAPHORA

(62) Def. 179: Coreferential (Anaphoric) Arc (A) Kernel Anaphoric Arc (A) Not (Copy Arc (A)). A few observations are in order about Definitions 177-79. We have not built into the definition of "Copy Arc" all the properties we have informally assumed. In particular, nothing in the definition itself specifies that the seconder of a copy arc is the successor in question, nor even that copy arcs are kernel anaphoric arcs. The latter is unnecessary if something specifies the former, since successor and predecessor necessarily overlap. We return to the question of the seconders of copy arcs below, showing that these are determined by theorem. Next, inherent anaphoric arcs cover all noncopy anaphoric arcs, not only those whose sponsors are members of the limited set of families called clans. We have little occasion to deal with inherent anaphoric arcs in general. We define the notion to locate our analysis within its proper wider context (so as not to lose sight of facts like those in, e.g., (56) above). The term "coreferential (anaphoric) arc" is, of course, misleading, but rather in accord with recent tradition. Coreferential arcs are, obviously, inherent anaphoric arcs, and the classes of copy arcs and coreferential arcs are complement sets which jointly ex­ haust the class of kernel anaphoric arcs. 13 There is no term to cover a logically possible class of anaphoric arcs, namely, nonkernel copy arcs. Although apparently allowed so far, we believe that no such arcs exist, and they are ruled out below (see Theorem 111). Given the definitions of anaphoric arc types, one can then for com­ pleteness and convenience define corresponding pronoun types:

13 One problem possibly caused by this binary division is that it leaves no obvious way to describe examples like: (i) M e l v i n did it by h i m s e l f . (ii) M e l v i n has h i m s e l f been arrested. Evidently there are anaphoric connections between the underlined forms. Yet it does not seem natural to treat the pronouns as heads of coreferential arcs, nor is there any obvious way they would be copy arcs (since it is unclear what successor/ predecessor pairs could be involved). Such cases remain highly problematic at this stage for the present theory of anaphora.

11.6. TWO TYPES OF ANAPHORIC CONNECTION

(63) a. Def. 180:

485

Pronoun (a)

b. Def. 181:

Anaphoric Pronoun(a)

c. Def. 182:

Dummy (Pronoun) (a)

d. Def. 183:

Kernel Pronoun(a)

e. Def. 184:

Copy (Pronoun) (a)

f. Def. 185:

Inherent Pronoun(a)

g. Def. 186:

Coreferential Pronoun(a)

~ (3A)(Head (a,Α) Λ

a. Pro Arc(A) b. Anaphoric Arc (A) c. Ghost(A) d. Kernel Anaphoric Arc(A) e. Copy Arc(A) f. Inherent Anaphoric Arc (A) g. Coreferential Arc(A) (63c), repeated from (10.7), is included here to situate dummy pronouns in the wider set of pronouns, a class to which they belong by virtue of the definition of "Pro Arc" (see section 10). Now we turn to the problem of what pairs of overlapping arcs can cosponsor kernel anaphoric arcs. Given that Cosponsor(A,B,C) and Kernel AnaphoricAre(C), what is the character of A and B? Weknowfrom previous considerations that in this situation C replaces one of JA, BS and is seconded by the other. Our informal claim was that either C is a copy arc or both A and B are self-sponsoring. We now make these claims precise. Definition 177 in (60) does not build into the notion Copy Arc all of the properties assumed for this notion. We earlier characterized copy anaphora informally as involving an anaphoric arc which replaces a prede­ cessor and is seconded by the successor of that predecessor. (60) defines a copy arc as any anaphoric arc which replaces a predecessor. This says nothing about the seconder and therefore allows copy arcs with seconders which are not the appropriate successors, or not successors at all. However,

486

11. REPLACERS AND ANAPHORA

this is not really allowed since copy arcs provably have the properties we have assumed. The key element here is PN law 8, The Predecessor Replacer Sponsor Law, stated in Chapter 5, which greatly limits the possi­ bilities for replacer cospotisors one of which is a predecessor. (64) THEOREM 110 (The Copy Arc Theorem) Replace(A t W) ACopy Arc (A) Λ Seconds (C,A) -> Successor (C,B) . Proof. Let A', B', C' be three arcs such that Replace (A', B'), Copy Arc (A'), and Seconds (C', A'). And assume the contrary of the conse­ quent. Therefore: (i) Sponsor (B', A') a Sponsor (C', A') ANot (Successor (C', B'). Since Copy Arc(A'), it follows from definition of "Copy Arc" that: (ii) (3D) (Successor (D, B') • Let D' be the successor of B'. By hypothesis, D'^ C'. And, since the successor relation is irreflexive, D' J= B'. From The Predecessor Replacer Sponsor Law: (iii) Sponsor (D', A') since this law says that that the successor of a replaced arc G sponsors the replacer of G. Butsince D'/ C' and D'^ B', (iii) and (i) together are inconsistent with The Maximal Two Sponsor Law. QED. (64) guarantees that the seconder of a copy arc is the successor of the arc the copy arc replaces. Hence: (65) THEOREM 111 (The Copy Arc Kernel Anaphoric Arc Theorem) Copy Arc(A) -» Kernel Anaphoric Arc (A) . Proof. Let A' be a copy arc. The definition of "Copy Arc" determines that there is some arc, call it B', of which A' is the anaphoric replace­ ment, and that B' has a successor, call it C': (i) Anaphoric Replacement (A', B') A Successor (C', B') . It then follows from Theorem 110 that C' seconds and hence sponsors A'. Hence from the definition of "Pronominalize": (ii) Pronominalize (A', B', C').

11,6. TWO TYPES OF ANAPHORIC CONNECTION

487

But since Successor(C', B'): (iii) Overlap (C', B'). And the conjunction of (ii) and (iii) is an instantiation of the defining ex­ pression for "Kernel Anaphoric Arc." QED. Hence, even though the definition of "Copy Arc" alone does not specify that copy arcs are kernel anaphoric arcs, this is necessarily true given other assumptions and the class of nonkernel anaphoric arc copy arcs is null. Informally, we stated in effect that noncopy kernel anaphoric arcs were replacers of self-sponsoring arcs. We now make this precise and even stronger: (66) PN Law 90 (The Coreferential Arc Law) Replace (A,B) ACoreferential Arc(A) -> (B). This formal principle is stronger than the informal account for the follow­ ing reason. The latter stated only that coreferential arcs replaced selfsponsoring arcs, hence via The Self-Sponsor Coordinate Law, arcs whose first coordinates are C 1 . PN law 90 goes beyond this to require that C1 also be the last coordinate of any arc replaced by a coreferential arc. (66) requires that coreferential arcs replace arcs which do riot fall through, and which are hence such that their first coordinate is their only coordinate. No parallel condition is (or should be) imposed on copy arcs, which can, as illustrated below, replace arcs unconstrained as to first and later coordinates. PN law 90 immediately entails that: (67) THEOREM 112 (The Coreferential Arc First Coordinate Theorem) Coreferential Arc (A) -> (A). Proof. Let A' be a coreferential (hence anaphoric) arc. From the defini­ tion of the latter, we know that (ΉΒ) (Replace (A', B)). Let B' be the re­ placed arc. From The Coreferential Arc Law it follows that (B'). Therefore, from The Replacer Coordinate Law requires that (A'). QED.

488

11. REPLACERS AND ANAPHORA

The development so far determines that the overlapping sponsors of an anaphoric arc (the sponsors of a kernel anaphoric arc) are either predeces­ sor and successor (with the predecessor the replaced arc) or else such that the replaced arc has only the coordinate C 1 . This leaves open the coordi­ nates of the seconding arc of an inherent anaphoric arc. We now impose narrow restrictions on this. The following claims are not limited to prefer­ ential arcs because, in this case, we know of no reason not to generalize beyond the case of clan sponsors to family sponsors: (68) PN Law 91 (The Inherent Anaphoric Arc Seconder Law) Inherent Anaphoric Arc (A) Λ Seconds (B,A) -> Self-Sponsor (B) . Let us see how recent definitions, PN laws, and theorems apply to some actual cases and what kinds of logically possible situations they preclude. First, with respect to copy arcs, return to an example considered earlier, the German clause: (69) Solche Sachen sagen sich nicht. such things say themselves not = "Such things aren't said." The relevant structure for this is: (70)

solche Sochen sich

sagen (nicht)

Definition 177 in (60) specifies that in this German reflexive passive clause, A is a copy arc, since it is an anaphoric replacement of an arc, B , which has a successor, namely C . Theorem 110 shows that the suc­ cessor, C , must second A , as it does. Via (63e), the nominal node

489

11.6. TWO TYPES OF ANAPHORIC CONNECTION

corresponding to sich is a copy pronoun, as desired. A erases B as re­ quired by The Replacer Erase Law. The replaced arc, B, in (70) has C1 as its only coordinate. Therefore, while all coreferential arcs must replace C 1 arcs, some copy arcs can replace C1 arcs. Nothing in the formalism precludes this. The definition of "Copy Arc" and Theorems 110 and 111 merely require that the two spon­ sors of a copy arc be successor and predecessor. They are silent on questions of coordinates. Consider then the following French example (from Ruwet [1972: 113]) involving both reflexive passivization and left dislocation: (71) Un criminel pareil, pa se juge. a criminal like that that self judges = "A criminal like that, he gets sentenced." This would involve the PN: (72) GR TOp/C;

GR

GR,

un criminel pareil

soi

se

juge

Concentrate on E , an anaphoric 1 arc which replaces C . C's only coordinate is c 2 . Because E has overlapping sponsors, it must be a copy arc, since it cannot, given PN law 90, be a coreferential arc. E is a copy arc, since the arc it replaces, C , is the predecessor of the Top

490

11. REPLACERS AND ANAPHORA

arc, B. As required by Theorem 110, this successor arc seconds E. (72) thus illustrates the earlier claim that there are cases where copy arcs re­ place non C1 arcs. H in (72) is also a copy arc but one exactly like A in (70). Consider some structural types that are precluded by the constraints on anaphora introduced so far. Many languages, e.g., Chichewa (see Trithart [1976]), have raising rules which involve copy pronouns, and which yield sentences of schematically the form: (73) a. Mary believes Jack that he sings = "Mary believes Jack to sing. b. Mary believes herself that she sings = "Mary believes herself to sing." where the italicized pronouns are the copies in question. In such cases, the copies are heads of arcs which replace 1 arc predecessors and are seconded by the upstairs 2 arc foreign successors of those 1 arcs, in accord with the principles imposed. It would a priori be possible for a language to have sentences like (73b) and not have those like (73a) if, for example, there were allowable structures like: (74)

sings Mary

herself

believes she

In this, the anaphoric arc E is a copy arc since it replaces D , which has a successor. However, the seconder of E is not the successor of

491

11.6. TWO TYPES OF ANAPHORIC CONNECTION

D, B, as required by Theorem 110, but A. Hence (74) is not an allow­ able structure since E is a copy arc with an improper seconder. In other words, E is formally a copy arc but is not intuitively a "copy arc" since its seconder is not a successor. Theorem 110 thus reconstructs the intui­ tion in question. Another example of the same sort of universally blocked "half copy arc" structure is provided by (75a), which would yield a sentence like (75b) (75) a.

P\C|Cg C 3

\

sang

I W2C3

her

(to) her

b. *Mary said Joe sang her a song to her. In this 3-2 advancement Structure, by Definition 177 in (60), E is a copy arc since the arc it replaces, B , has a successor, C. However, E is not an intuitive "copy arc" since its seconder is not the successor of B , but rather A. (75a) thus also violates Theorem 110 and, like other struc­ tures of this sort, is precluded by the present theory. Structures like (74) and (75a) are not obviously in conflict with any other principles governing anaphoric arcs besides Theorem 110. For in­ stance, although E in (75a) contradicts Theorem 110, it is an anaphoric 3 arc of a complement seconded by a main clause 1 arc. This is a pattern independently attested in well-formed structures, e.g., in (76a) whose PN is (76b):

492

11. REPLACERS AND ANAPHOKA

(76) a. Mary said Joe sang a song to her. b.

said

Mory

sang (to) her Joe

a song

Moreover, it cannot be claimed that representations like (75a) are indepen­ dently blocked due to, e.g., the fact that a single arc, there A , seconds two distinct arcs, D and E. Fortherecanbenoprincipleprecluding

this. Consider (77a), which, on the relevant reading has the PN in (77b): (77) a. Joe scratched himself and then he covered himself. b Con

scratched

himself

Con

Joe himself

covered

In this, D seconds both B and H, without iU-formedness resulting. We conclude that Theorem 110 and PN law 8 which underlies it make a sub­ stantial contribution to eliminating unattested anaphoric structures in which anaphoric arcs which formally meet the conditions of the definition of "Copy Arc" have seconders which are not successors of the arcs which are replaced.

11.6. TWO TYPES OF ANAPHORIC CONNECTION

493

Next, consider the constraints imposed on the sponsors of coreferential arcs. These are that an arc replaced by a coreferential arc have no coordinate other than C 1 and that the seconder have the first coordinate C 1 . The latter claim, embodied in PN law 91, applies indifferently whether the seconder is a neighbor of the inherent anaphoric arc or not, since PN law 91 imposes no requirements in this regard. The most obvious implication is that no coreferential arc can replace a non C 1 arc and thus, in particular, not a successor or a graft. Since replacers are grafts, coreferential arcs cannot replace other replacers, or ghost arcs. (78) THEOREM 113 (The First Coreferential Arc Replacee Theorem) Coreferential Arc(A) λ Replace (A,B) -» /Voi((3C) (Successor (B ,C)) . Proof. Let A' be a coreferential arc and B' the arc it replaces. Suppose, contrary to the consequent, that B' is the successor of some arc. Then it follows from The Self-Sponsor Law that B' is not self-sponsoring, and from The Self-Sponsor Coordinate Law that B's first coordinate is not C 1 , contradicting PN law 90, The Coreferential Arc Law. QED. (79) THEOREM 114 (The Second Coreferential Arc Replacee Theorem) Coreferential Arc(A) A Replace(A l B) -> Not(Graft(B)). Proof. Let A' be a coreferential arc and B' the arc it replaces. Suppose, contrary to the consequent, that B' is a graft. Then it follows from The Self-Sponsor Law that B' is not self-sponsoring and from The SelfSponsor Coordinate Law that B's first coordinate is not C 1 , contradicting PN law 90, The Coreferential Arc Law. QED. These results rule out vast numbers of otherwise allowed structures. Let us concentrate on the implications of Theorem 113. Consider pairs like: (80) a. (i)

Melvin wrote a letter to Betty.

(ii) Melvin wrote Betty a letter.

494

11. REPLACERS AND ANAPHORA

b. (i) Melvin wrote a letter to himself. (ii) Melvin wrote himself a letter. In accord with previous RG work, we take the (i) and (ii) examples in these pairs to involve the same self-sponsoring arcs. But they differ in other arcs, namely, those characterizing 3-2 advancement constructions and those due to The Chomeur Law. In APG terms, (80a, ii) involves Betty as the head of a 2 arc local successor of a 3 arc, and a letter as

head of a Cho arc local successor of a 2 arc. The interaction of this view with the overlapping arc replacer concep­ tion of "coreferential" anaphora would a priori generate multiple possible structures for an example like (80b, ii). We take this to have the correct PN: (81)

Melvin

α letter

t

himself

wrote

The key element is that the anaphor himself is introduced as a 3, not as a 2. The italicized concept here is convenient, and can be formally defined (82) Def. 187: Introduced as (a, GR x ) arc, as PN law 90 requires. It is then G , not the 3 arc which G replaces, B ,

495

11.6. TWO TYPES OF ANAPHORIC CONNECTION

which has the 2 arc successor defining a 3-2 advancement structure. Without PN law 90, however, nothing in previous assumptions would block an additional structure for (80b, ii), namely: (83)

α letter himself

wrote

In (83), G is a 2 arc entrant, which replaces a arc, C. Since G is not a copy arc, this contradicts PN law 90, and (83) is not a well-formed PN. Thus, PN law 90 rules out otherwise possible distinct structures for the "same" clause. This law claims, inter alia, that coreferential arcs are determined completely independently of the set of all successors. We have not given any justification for PN law 90 other than its restrictiveness; in particular, we have not justified it against other restric­ tive principles which might be incompatible with it. We will, however, show how PN law 90 deals with a class of problems which might otherwise be taken to be a difficulty for the underlying view that overlapping selfsponsoring arcs reconstruct the notion of "coreference." Hankamer (1976), operating in a transformational framework, attempts to show that there are such things as "deep" anaphors, by which he means, roughly, anaphors which have no syntactic structure distinct from their surface forms, more particularly, that there are anaphors which are not de­ rived from "full nominals." This is translatable into APG terms as a claim that there are anaphoric arcs whose heads are understood as

11. REPLACERS AND ANAPHORA

496

"coreferential" to the head of arcs defining a clan but which are not sponsored by members of that clan. Hankamer gives arguments to support his view, arguments showing that there are anaphors which behave syntactically in a way which indi­ cates their lack of fuller syntactic representation. One argument he takes from Witten (1972). It involves the interaction of pronominalization with the English extraposition construction. The key points, ignoring aspects with no APG relevance or translation, are these. Extraposition requires clausal subjects. So the impossibility of extraposed examples like (84b) alongside nonextraposed examples like (84a) would follow directly from the view that "coreferential" anaphors have no deeper syntactic repre­ sentation: (84) a. That he was incompetent soon became clear and it/that didn't surprise me. U t b. *T That he was incompetent soon became clear and it didn't n

surprise me it/that. This argument seems to have force even in APG terms. For there is nothing to block the case where a single node corresponding to an other­ wise extraposable complement would be the subject of a main clause and also the extraposed subject of another. The Cho arc determined by extra­ position could then be replaced by an anaphoric arc, yielding, e.g., (84b). A priori, nothing in APG terms would block structures like the following, with the complement represented as earlier with a triangle: (85)

it/that

11.6. TWO TYPES OF ANAPHORIC CONNECTION

497

However, while nothing a priori blocks structures like (85), they are effec­ tively excluded by PN law 90, since structures like (85) contradict Theorem 113. For the anaphoric arc D is not a copy arc (since the arc it replaces has no successor). Hence, it must be a coreferential arc (since it is a kernel anaphoric arc). Therefore, Theorem 113 precludes the possibility that D could replace an arc which is a successor. But in (85) D replaces C, which is B's successor. Hence, (85) is rendered illformed by Theorem 113. More generally, speaking informally, Theorem 113 renders it impossible for "pronominalization to operate on the output of extraposition." The arc replaced by a coreferential arc cannot be a Cho arc local successor determined by extraposition, as a special case of the fact that the replacee of a coreferential arc cannot be a successor of any kind. We can phrase this somewhat differently. It is, of course, possible, as already illustrated by, e.g., C in (72), for a successor to have an anaphoric replacement. But in these cases, the anaphoric replacement must be a copy arc: (86) THEOREM 115 (The Successor Anaphoric Replacement Theorem)

Successor (B,C) Λ Anaphoric Replacement (A,B) A Kernel Anaphoric Arc (A) -> Copy Arc (A) . Proof. Let B' be the successor of C' and A', an anaphoric replace­

ment of B' which is a kernel anaphoric arc. The definition of the latter concept determines that the cosponsors of A', one of which is B', over­ lap. Assume the contrary of the consequent. Hence Not (Copy arc(A')). It then follows from the definition of "Coreferential Arc" that A' is a coreferential arc. Theorem 113 entails that B' is not a successor, contra­ dicting the assumption that B' is the successor of C'. QED. Since no successor can be replaced by a coreferential arc, the analogue of the structure discussed by Hankamer and Witten for examples like (84b) is provably impossible in a version of APG theory embodying PN law 90.

498

11. REPLACERS AND ANAPHORA

Analogous remarks hold for cases like: (87) *1 like some cats and there's them on the roof. discussed first in Bresnan (1970) and also taken by Hankamer (1976) to support the same claim supported by those like (84b). The identical principle also blocks the analogous structure for examples like (88b): (88) a. I heard about the things they are doing in Cleveland and they are terrible. b. *1 heard about the things they are doing in Cleveland and it's terrible them. c. It's terrible the things they are doing in Cleveland. In all these cases, undesirable structures are blocked by the principle that a well-formed PN cannot involve a successor arc replaced by a coreferential arc. However, PN law 90 does not block examples like (84b), (87), and (88b) per se, but only certain structures. There are fheory-unblocked structures for all these examples in which the entrant anaphoric arc re­ places a nonsuccessor and is thus itself the predecessor of a Cho arc. Thus, while Theorem 113 blocks structure (85), neither it nor any other principle precludes: (89)

surprised it/that

it

This structure also determines (84a). But unlike (85), it does not contra­ dict Theorem 113, since the coreferential arc C replaces a Cj arc, B.

11.6. TWO TYPES OF ANAPHORIC CONNECTION

499

Therefore, the ill-formedness of (89) is not a function of universal grammar and must be attributed to a-property of English. Informally, this is the fact that extraposition is limited to clausal nominals, a condition not met by either the pronouns it or that. More precisely, the arc sponsoring a stable ghost arc whose head corresponds to an extraposition dummy it must have a head corresponding to a complement clause (of a certain type). Hence, the pair Sponsor(CjE) is an illegitimate sponsoring of a ghost arc from the point of view of this English-particular restriction. Analogous remarks hold for (87) and (88b), although it is less clear what English condition is involved. For (87) it may simply be definiteness, on the assumption that anaphoric pronouns are definite and that the dummy there construction in question requires that the sponsor of its de­ fining ghost arc be headed by an indefinite nominal. Interestingly, a dif­ ferent dummy there construction in English, which is indifferent to definiteness, is not incompatible with coreferential pronouns: (90) a. Who should we invite to the party. There's Tom. b. Tom was asking who we should invite to the party. Well, there's him.

We would propose a PN fragment for structures like there's him of the form:14 (91)

there

14 We ignore here the possibility of an unaccusative initial analysis of the iiondummy nominal.

500

11. REPLACERS AND ANAPHORA

If correct, such structures support the idea that nothing universal blocks sentences of, e .g., the form (87), which then involve language-particular idiosyncracies. We conclude that the type of argument surveyed by Hankamer does not, in the presence of a principle like PN law 90 and its implication, Theorem 113, in any way throw doubt on the idea that "coreference" is properly reconstructible in terms of overlapping self-sponsoring arcs. Given these principles, the facts showing the "syntactic inertness" of anaphoric prono'uns are predicted, even under the conception of "coreference" in ques­ tion. PN law 90 then receives some initial justification. We have said nothing so far bearing on PN law 91, which requires the seconding arc of an inherent anaphoric arc to be self-sponsoring and thus to have first coordinate C 1 . This is a weaker requirement than that im­ posed on the arcs replaced by coreferential arcs, for the latter are required by PN law 90 not only to have coordinate sequences which begin with C 1 but which also end with C 1 . Like PN law 90, the initial function of PN law 91 is to preclude multiple analyses for various anaphoric cases. Con­ sider the example (92) with proper PN (93): (92) Melvin was told by Mary that he was lazy. (93)

°2

Cho/c (was) told

(by) Mary Melvin

(was) lazy

Herethecoreferentialarc J is seconded by the upstairs C 1 arc E, in accord with PN law 91. Without that law, (92) would also be representable

11.6. TWO TYPES OF ANAPHORIC CONNECTION

501

by structures otherwise like (93) but with the seconding arc being either D or C . The present theory thus claims that successors in such cases are necessarily irrelevant to "coreferential" anaphora. Put differently, the theory now requires a sentence like (92) to contain exactly the same coreferential arc sponsors as an ill-formed structure like: 15 (94) *Mary told that he was lazy to Melvin. In this, arcs corresponding to C and D in (93) do not exist. The implication of PN laws 90 and 91 is thus that the three arcs in­ volved in a coreferential arc cosponsor situation are always maximally "early" arcs. The anaphoric arc itself must be a c 2 arc, the replaced area arc, and the seconder a arc. Theoverallresultis that no syntactic rules involving successors, etc., will be able to treat the replaced arc in such cases as present. More precisely, this arc can be referenced only by rules referring to self-sponsoring arcs. Other rules will, in effect, treat the replacee of a coreferential arc as nonexistent.

11.7. Further remarks on kernel anaphoric arcs We make explicit a few immediate consequences of our treatment of anaphora involving overlapping arcs, that is, anaphoric arc sponsors which are members of a clan. These consequences are relevant to McCawley's comments, quoted in section 5, about the difficulties of "disconnecting" overlapping arcs. We pursue this problem from a different point of view in section 9. Any kernel anaphoric situation involves a minimum of three pairs, name­ ly, one sponsor pair linking the anaphoric arc to each of its overlapping sponsors, and one erase pair linking the anaphoric arc to the arc it replaces. Schematically:

The ill-formedness of (94) is irrelevant to present concerns, being a func­ tion of an English constraint, never adequately formulated in any terms, barring certain "internal" complements. See Ross (1967a), Kuno (1973b) for discussion.

502

11. REPLACERS AND ANAPHORA

(95) Kernel Anaphoric Arc

b a

There are two subcases of (95), depending on the relations between A and B . In one case, A and B are a successor/predecessor pair and C is a copy arc. In the other, A and B are self-sponsoring and C is a coreferential arc. However, in either case, C replaces B . Thus The Replacer Erase Law guarantees that C erases B . Theorem 7 in Chapter 5 shows that replacees are never surface arcs. Consequently, arcs,replaced by kernel anaphoric arcs of either the copy or coreferential variety are not surface arcs. Moreover, the Erase pairs which determine this need not be specified by language-particular rules since they follow from: (96)

THEOREM

116 (The Kernel Anaphoric Arc Replacee Erasure Theorem)

Kernel Anaphoric Arc(A) a Anaphoric Replacement(A,B) -» Erase (A,B). Proof. Immediate from the definitions and The Replacer Erase Law. QED. Therefore, what needs saying (vis-a-vis situations like (95)) in particu­ lar languages involves at most specification of the possibility of the spon­ sor pairs. However, here also, a great deal has already been extracted. If B is a predecessor, then A must be its successor. And if B is not a predecessor, both A and B must be self-sponsoring arcs, with B's last coordinate being C 1 . Left open is the question of which (subset of) arcs in a given clan with η self-sponsoring members have coreferential arc replacers. In gen­ eral, this question involves the problem of "pronominalization constraints" and is beyond the purview of this account. However, we can make one further observation of a universal character. It follows from Theorem 109,

11.7. REMARKS ON KERNEL ANAPHORIC ARCS

503

The Anaphoric Replacement Limitation Theorem, that not all members of a clan can have anaphoric replacers. This precludes, inter alia, bizarre structures of the form in (42), which we repeat:

himself

Joe

himself

tickled

(97) raises, however, the possibility that the explanation of the illformedness of the sentence it determines, namely : (98) *Himself tickled himself. via Theorem 109 is not entirely satisfactory. For it might be argued that (97) violates a deeper and more general requirement on PNs, one which would prevent all members of certain kinds of clans from being assassi­ nated, independently of any questions of anaphoric arcs. Nothing in the explanation of the impossibility of (97) via Theorem 109 would account for the impossibility of PNs with substructures of the form:

Joe Obviously this kind of unhooking situation is not precluded by any con­ straints on anaphora or anaphoric chains, since no anaphoric arcs are present. Moreover, otherwise similar unhooking situations do, we assume, exist, e.g., in equi structures (see (38) above).

11. REPLACERS AND ANAPHORA

504

We can characterize structures like, inter alia, (99) better if we have the following concept: (100) Def. 188: Survivor(A) «-» Not((3B)(Assassinate(B,A))). That is, survivors are arcs which are not assassinated. Hence, a survivor is an arc which is either not erased, and is hence a surface arc, or which self-erases. Survivors are, therefore, all final stratum arcs. Structures like (99) can then be taken to illustrate cases where clans containing over­ lapping arcs of a certain type fail to have survivors. If, as seems reason­ able, structures of the form (99) are not in general possible, there are grounds for a law which would specify directly the need for a survivor in such cases. The hedges in the above remarks are due to the need for at least two restrictions. It seems that only clans containing self-sponsoring arcs are subject to some kind of survivor condition. Clans containing a graft en­ trant apparently can fail to contain a survivor (see H in (72), which is a member of a [uni]clan with no survivor). Secondly, recalling the discussion of Chapter 9 and the division of nodes into members of Explicit and Inex­ plicit, the constraint in question could consistently be required only of clans whose arcs are headed by members of Explicit. We gave analyses in Chapter 9 (see (9.51)) in which clans with arcs headed by members of Inexplicit had no survivors. This is connected to the greater freedom of zeroing allowed by The Nominal Arc Zeroing Law, PN law 76, for arcs headed by members of Inexplicit. It seems that the strongest principle one could suggest, given other APG assumptions at this point, would be limited to clans containing at least one self-sponsoring arc and to clans whose arcs are headed by members of Explicit. To state the relevant constraint more elegantly, we define: (101) Def. 189: P r i m a l ( C l a n ) ( X ) (3A) (A c X Λ Survivor (A)) . On the assumption that SA, B, Cj in (99) forms an explicit, primal clan, such structures are then blocked by PN law 92, although not by any previ­ ous considerations. (99) is an instantiation of a situation which may be blocked indepen­ dently of questions of clan survivors. In (99), C assassinates A, while C is in turn R-assassinated by A . It follows that (99) would be blocked by a law parallel to PN law 6, The Sponsor Independence Law, which pre­ cluded this kind of "assassination loop." Since we know of no cases of this sort, we suggest: (104) PN Law 93 (The Assassination Independence Law) Assassinate (A,B) -» Not(R-Assassinate(B,A)) . PN law 93 blocks structures like (99) independently of (103). Since struc­ tures like (97) are also blocked independently of (103), possibly (103) might ultimately be a theorem. However, this remains a conjecture. It is easy to construct structures which contradict (103) but which violate neither The Assassination Independence Law nor The Anaphoric Chain Law, e .g.: (105)

Joe

α

At the moment, to block structures like (105), one would at best have to appeal to the various laws about zeroing in Chapter 9. But it is by no means clear that these preclude all such situations. Moreover, (103) is

506

11. REPLACERS AND ANAPHORA

not limited to clans containing Nominal arcs. Hence, it is not evident that (103) is provable. A final word about (103). This principle does not require that at least one member of a primal explicit clan be a surface arc. It permits erasure of the minimum one survivor as long as this is via self-erasure, since arcs which self-erase are survivors. In other words, even with PN law 92, we are in principle allowing the deletion of the node which is the head of all the arcs in a primal explicit clan. But this deletion is subject to the strict (though so far unformalized) constraints on heads of self-erasing arcs. Since we suspect informally that arcs headed by members of Ex­ plicit are not in general subject to self-erasure, PN law 92 will, when sup­ ported by proper constraints on self-erasure, ultimately require that primal explicit clans have at least one member which is a surface ate. Hence, although PN law 92 alone allows primal explicit clans which contain no surface arcs, our suspicion is that a proper overall APG theory ultimately will preclude this.

11.8. Parallelisms between coreferential arcs and copy arcs The account of kernel anaphoric arcs developed above provides the basis for an explanation of a traditional observation about clause structure which has long puzzled grammarians. Informally, this is the tendency for (some types of) passive clauses in many languages to have the form of reflexive clauses. See, for example, Sweet(189l: 114). This problem has been emphasized in recent times by Langacker (1970,1974) and Langacker and Munro (1975), who have stressed that a valid theory of clause structure should provide a basis for this phenomenon. We attempt to show that the APG account of anaphora meets this requirement. The problem can be introduced by considering an ambiguous French clause like: (106) Un robot a

se

lave

souvent.

robot self washes often.

507

11.8. C(PREFERENTIAL ARCS AND COPY ARCS

On one reading, (106) is an ordinary reflexive structure, and means fiA robot washes itself often." On the other, it is a reflexive passive, and means something like "One washes a robot often."16 In APG terms, these involve the respective PNs:

GR GR1 GR1

un robot

se

SOf

fdve

souvent

(108)

souvent

GR, GR un robot

soi se

love

(107) is essentially like the structure discussed at the beginning of this chapter, i.e., like (2).17 In it, A and B cosponsor the replacer C. By the definition of "Arc Antecede", A arc antecedes C and un

16 An

robot pto-

interesting study of this construction in French is found in Ruwet (1972: Chapter 3). 17 We ignore in (107) an antipassive analysis of French reflexive clauses to account for the intransitive behavior in clause union constructions, as argued in Postal (1977). If such an analysis is correct, then A in (107) would have a 2 arc local successor, this arc would have a 1 arc local successor, and C would have a Cho arc local successor. A more complete representation in these terms would be:

508

11. REPLACERS AND ANAPHORA

nominally antecedes soi. A and B are self-sponsoring arcs and hence the overlapping arcs which cosponsor the replacer are members of the L-graph of the sentence. The structure in (108) is largely parallel to that in (107), with crucial differences however. In particular, the overlapping cosponsors of the replacer C are not self-sponsoring. Rather, the replaced arc, B is a prede­ cessor. While C in (107) is a coreferential arc, C in (108) is a copy arc. Hence, in accord with Theorem 113, the cosponsor of C in (108) is the successor of B, A . (108) thus contains one more arc than (107) because it has a local successor which (107) lacks.

GR-

GR. GR,

un robot

soi

lave

se

souvent

Note 28 of Chapter 8 observed, a propos of an antipassive analysis of cases in­ volving 2 arcs headed by UN nodes, that an a priori possible direct object retreat treatment was blocked by virtue of'the principle precluding UN nodes from heading distinct (nonbinder) arcs. However, the same considerations do not hold here. There is nothing in principle so far precluding the possibility that, instead of (i), the structure yielding final in transitivity for sentences like (106) involves a 3 arc local successor for the pronominal 2 arc:

(U)

GRGR. GR i

un robot

SOl

se

love

souvent

From several points of view, including overall simplicity and the ease of describ­ ing the cliticization of se, structures like (ii) may actually be preferable to those like (i).

11.8. COREFERENTIAL ARCS AND COPY ARCS

509

Structures like (107) and (108) share the following features: (109) a. In both a kernel anaphoric arc, C , is cosponsored by two parallel arcs, A and B. b. The replaced arc, B , is a 2 arc, and the seconder, A , is a neighboring 1 arc. c. The survivor (and seconder) is a 1 arc. d. The replaced 2 arc is erased by the replacer, via The Replacer Erase Law. The key difference is that in one case the cosponsors of the replacer are self-sponsoring arcs, in the other predecessor and successor. The two cases illustrate the two types of kernel anaphoric arc sponsoring possible in the present theory. APG theory accounts for the similarity of ordinary reflexives and re­ flexive passives in a straightforward way. What is crucial is an account of reflexive passives which takes them to involve copy 2 arcs sponsored by the accusative 2 arc whose 1 arc local successor defines the passivi­ ty of the structure. Given this, both ordinary reflexives and reflexive passives will generate parallel anaphoric chains, and hence parallel arc antecedence and pronominal antecedence connections. In (108), the initial 1 arc headed by an O node is zeroed by the over­ running 1 arc characteristic of the passive construction. This is lawful in French. However, it is not required by any principles we have stated.

Nothing in APG theory universally precludes the possibility that reflexive passives have Cho arc local successors of 1 arcs like D in (108). And this freedom is a virtue. For, although well-known cases of reflexive passives are like French in not permitting chomeuts, there are attested cases where reflexive passives do involve chomeurs, e.g., in Lardil (see Klokied [1976]). 18 18

^

Moreover, Ruwet(1972: 110) observes in effect that chomeurs were possible at earlier periods: (i) was acceptable in eighteenth-century French: (i) Cela se dit par Ie peuple. that self says by the people = "That is said by the people."

510

11. REPLACERS AND ANAPHORA

In summarizing the APG explanation of the morphosyntactic similarity between reflexive passives and ordinary reflexive clauses, we find that the theory allows kernel anaphoric arcs to be cosponsored both by pairs of self-sponsoring arcs and by successor/predecessor pairs. If the two arcs are parallel 1 and 2 arcs, with the 1 arc a survivor, the two struc­ tures are formally extremely similar. The structures relevant for anaphoric chains and arc antecedence will be identical. Moreover, The Replacer Erase Law will necessarily function in parallel ways in the two cases. The explanation is, in short, that copy arc structures and coreferential arc structures are necessarily largely isomorphic, given R-sign parallel­ isms between their cosponsors. The parallelism between ordinary reflexives and reflexive passives is only the tip of an iceberg of related similarities, all due to the extensive isomorphism between kernel anaphoric arcs cosponsored by self-sponsoring arcs and those cosponsored by successor/predecessor pairs. Such situa­ tions are by no means limited either to passivization or even to pairs of cosponsors which are neighbors. In principle, one should find such simi­ larities in every circumstance where it is possible for two arcs to cosponsor a kernel anaphoric arc. The same parallelisms show up in unaccusative cases. In cases where an unaccusative 2 arc has a 1 arc local successor, it is possible for these to cosponsor a copy arc. This will yield structures parallel to reflexive passives and ordinary reflexives. Hence in French one finds (110) whose PN is (111): (110) Les branches se brisent. the branches self break = "The branches break."

11.8. COREFERENTIAL ARCS AND COPY ARCS

511

Ies branches

soi

se

bris

Such unaccusative structures are isomorphic in the relevant respects to both ordinary reflexive structures like (107) and reflexive passives like (108), accounting for the morphosyntactic similarity of all three. The ex­ planation given offers a new type of motivation for taking reflexive struc­ tures like (110) to involve initial unaccusatives. Without this assumption, the parallelism with (107) and (108) would collapse. There would not be an explanation of the parallelism if one took Ies branches to correspond to the head of an initial 1 arc. All the cases of parallelism considered have involved kernel anaphoric arcs cosponsored by neighboring, hence parallel, arcs. Moreover, in all cases, the two arcs have been Nuclear Term arcs, and the survivor has been a 1 arc. While it is not provable that these are necessary properties of the types of construction under discussion, one can show, by appeal to PN law 50, The Demotion No Replacer Law, that various types of con­ struction cannot manifest the copy arcs required to permit successor cases to be relevantly isomorphic to self-sponsor cases. In current terms, the similarities in question are due to the fact that copy arcs have properties parallel to coreferential arcs. Both types are replacers. Hence, the kind

512

11. REPLACERS AND ANAPHORA

of similarities of interest here can only exist for arcs of the type which can cosponsor replacers. But recall PN law 50: (112) PN Law 50 (The Demotion No Replacer Law) Local Successor (A j B)AOutrank (B 1 A) -> Not ((3C)(Replace (C,B))). This law obviously precludes cosponsoring of copy arcs by local successor/ predecessor pairs in all six possible demotion cases of the form: 19 (113)

Predecessor

Local Successor

a.

1 arc

2 arc

b.

1 arc

3 arc

c.

2 arc

3 arc

d.

Term arc

Cho arc

(113a) defines antipassive constructions, (113b) defines inversion con­ structions, (113c) defines direct object retreat constructions, and (113d) defines all cases involving domestic Cho arcs. PN law 50 then predicts that, in contrast to, e.g., passive constructions, these six types of local demotion structures cannot have copy variants. But here one must be quite precise. The law in question precludes the situation where, e.g., with respect to (113a), the 1 arc and its 2 arc suc­ cessor cosponsor a copy 1 arc. However, since, as observed earlier, antipassivization "feeds" The Unaccusative Law, the 2 arc in question will have a 1 arc successor. Nothing precludes this predecessor/successor pair from cosponsoring a copy arc replacer of the 2 arc. We claim that this in fact is found, e.g., lexically determined, in French in cases like: (114) Pierre

s'attaquera

a

la

reine.

Pierre self-attack-will to the queen = "Pierre will attack the queen."

19

Other logically possible demotion types, e.g., Term arcs having Oblique arc local successors, are blocked by previous principles; see PN law 49, The No Oblique Successors Law, in Chapter 7.

513

11.8. COREFERENTIAL ARCS AND COPY ARCS

We suggest that this is an antipassivized clause with a PN of the form: (115)

® ΛΛΛΛΛΛΜΛΛΛΛ/

Pierre

(a) Io reine

s'

attaquero

PN law 50 precludes the possibility that A and B in (115) cosponsor a copy 1 arc. However, it does not preclude that B and C cosponsor the copy arc D , because in this successor/predecessor pair, (C, Β), the predecessor does not outrank the successor. (115) really involves the same kind of reflexive unaccusative structure as (111), since the seconder of the copy arc is a 1 arc successor of an unaccusative arc, determined by The Unaccusative Law. Hence antipassive constructions can be re­ flexive, as (114) is. But the reflexive will be determined by the unaccusa­ tive advancement successor and correspond to a copy 2 arc, as in simpler unaccusative structures. In the same way, inversion structures can, given (114b), not be such that a 1 arc and its 3 arc local successor cosponsor a copy 1 arc replacer of the 1 arc. However, when inversion constructions also involve ghost arcs, the ghost unaccusative 2 arc can, with its 1 arc successor, jointly sponsor a 2 arc copy, as in simpler unaccusative cases. We have already illustrated this for the Russian impersonal inversion construction in (10.30). Thus, inversion constructions can involve copy arcs, but these will be cosponsored by unaccusative arc/1 arc pairs, not by 1 arc/3 arc pairs, and the copy arc will be a 2 arc, not a 1 arc. Thus, the kind of copy arc cases attested seem to conform to the predictions of PN law 50, providing initial support for this view. This law could be overthrown by

514

11. REPLACERS AND ANAPHORA

finding a language otherwise like English which has sentences of, e.g., schematically the form in (116a) with the meaning of (116b): (116a) a. Herself slept to Joan. b. Joan slept. For cases like (116a) would involve copy 1 arcs cosponsored by a 1 arc and its 3 arc local successor. The claims in (113d) which preclude the possibility that a Termx arc and its Cho arc local successor could cosponsor a Termx copy arc seem well founded. This precludes otherwise normal passive PNs of the form in (117):

Cho

herself

Joari

Joe

(was! found

Strictly speaking, PN law 50 is not necessary to block such structures since they violate The Stratal Uniqueness Theorem, which was proved in­ dependently of this PN law. This would be true of any structure in which a Cho arc local successor seconded a copy arc.^®

(i) THEOREM 126 (The Cho Arc Copy Arc Seconding Theorem) Local Successor(A j B) ACho arc(A)ACopy arc(C) Λ Seconds (A, C) -» (3k) (3D) (Term x arc (C Λ D) Λ C JC (CAD) Λ Neighbor (C, D)) . Proof. Let A be a Cho arc successor of B' and C' a copy arc seconded by A'. It follows from the definition of "Copy arc" that C' replaces the predecessor of A', namely, B': (a) Local Successor (A', B') ACho arc A'AReplace (C', B') . Assume with no loss of generality that: (b) < d C j >(B').

11.8. COREFERENTIAL ARCS AND COPY ARCS

515

Unattested cases like (116a) violate not only PN law 50 but also standard "pronominalization constraints," which tend to require the sec­ onder to outrank the anaphoric arc. There may be a deeper connection between this kind of fact and PN law 50 than we have been able to bring out. So far, nothing in the current formalism embodies such connections. The parallelism between reflexive passives and ordinary reflexives is only a special case of the general large-scale (though not perfect) isomor­ phism between copy arcs and coreferential arcs. One thus expects such parallelisms in all contexts where successor/predecessor pairs can have R-signs identical to the R-signs of pairs of self-sponsoring arcs, and where both can cosponsor replacers. Hence, it is the same isomorphism which accounts for the parallelism between raising cases involving copies and coreferential cases, e.g., the parallelism between: (118) a. Joe looks like he is sick. b. Joe says he is sick. We would provide these with the respective PNs:

Hence, via The Local Successor Coordinate Law: (c) (A'). Then, since A' is a Cho arc local successor of B', The Chomeur Law determines that: (d) (3D) (cJ +J -Overrun (D, B')) . Let D' be the overrunner of B'. Hence: (e) Termx arc (D'A Β') ANeighbor (D' B') Ac.+j(D ) . From the fact that Replace (C' B'), from (b) and from The Replacer Coordinate Law: ( f ) < C j + ^ y>(Cr)A Same-Sign(c', B'). Moreover, since C' replaces B', C' and B' are neighbors, and thus C' and D' are. Hence: (g) Termx arc (C'AD') ACJ+J(C'A D') ANeighbor (C', D') . QED. Therefore, in all cases where a Cho arc seconds a copy arc, a stratal unique­ ness violation ensues. Hence, the current theory blocks examples like (117) in the text independently of PN law 50.

516

11. REPLACERS AND ANAPHORA

(119)

Cho\c2C3 C| C 2 C 3

fl c 2 (is) sick Iooks(Iike)

(120)

says

In (119) the kernel anaphoric arc, G, is cosponsored by the successor/ predecessor pair, (Β, Ε), an upstairs 2 arc and a downstairs 1 arc. G is thus a copy arc. In (120) the kernel anaphoric arc, C , has as cosponsors the self-sponsoring arcs A and B , an upstairs 1 arc and a down­ stairs 1 arc. However, the principles defining anaphoric chains and arc antecedence yield identical results in these cases. For B in (119) has a successor 1 arc, which erases it. Hence, A is the survivor in the anaphoric chain for (119), even though it is not a seconder of any anapho­ ric arc. As (118) illustrates, cases of coreferential arc/copy arc parallelism are not at all limited to cases where the anaphoric arcs are seconded by

11.8. COREFERENTIAL ARCS AND COPY ARCS

517

neighbors. Both local and foreign seconding yield (partial) isomorphisms of the relevant sort. Thus, the traditionally recognized similarity between, e.g., reflexive passives and ordinary reflexive clauses should be regarded as a special case of more general similarities between copy arcs and coreferential arcs. To conclude this section, we observe that, in some constructions in­ volving successors, sponsorship of a copy arc by the successor/predeces­ sor pair is required, in others it is impossible, and in others, possibly, it is optional. APG universal grammar simply allows any of these choices. Individual grammars must then specify the possibilities for copy arcs. For instance, in the English passive construction, copies must be blocked; in the English raising construction with verbs like believe, copies must be blocked: (121) a. I believe Joe to sing. b. *1 believe Joe for him to sing. On the other hand, in the raising construction in (118a), copies are required (122) *Joe looks like is sick. We address very briefly the question of how these contrasts are speci­ fied in grammars, or rather, we address this question to the extent that this is possible independent of a study of rule formulations that is not ever raised until Chapter 14. One of our goals is to redeem the claim made in Chapter 5 that the description of successors with copies provided one motivation for our treatment of the interaction of The Replacer Erase Law and The Successor Erase Law, that is, for letting the former be more general. Recall that these two laws determine for a pair: (123) Successor (A, B) that either:

(124) a. (3C) (Replace(C,B) Λ Erase(C 1 B), or b. Erase (A, B).

518

11. REPLACERS AND ANAPHORA

Copy arc cases fall exclusively under (124a). Whenever an arc, B, and its successor cosponsor a copy arc, that copy arc will erase B, via The Replacer Erase Law. Therefore: (125) Otherwise parallel successor constructions which differ as to the presence or absence of copy arcs which replace the predecessor can in all cases be characterized as follows: a. Noncopy Arc Cases (e.g., those like the English passive con­ struction) are those where: Successor(A, Β)

λ

Erase(A, B).

b. Copy Arc Cases (e.g., those like the English construction in (118a) are those where: Successor(A, Β) Λ Not(Erase(A, B) . In other words, given the present formulation, individual grammars can distinguish the two types of construction merely by reference to whether or not the successor erases its predecessor. If the language requires this, then no copy is possible, if the language requires that this not be the case, then a copy is required,21 and if the language says nothing, copies will be optional. 21

There is a partial oversimplification here. The reason is that arcs fail to be erased by their successors not just when they have copy arc replacers, but when they have any replacers at all. Hence, it would not be strictly true, as claimed in effect in (125), that all instances of failure of a successor to erase its predecessor involve copy arcs, unless one blocked other types of replacers for predecessors. This is not possible since our treatment of, inter alia, nominal flagging (see Chapter 13) involves noncopy arc replacers (closures) for some prede­ cessors. This does not really undermine the present discussion since (i) the class of successors which involve noncopy arc replacers for their predecessors is highly restricted, possibly to two types of arcs, Marq arcs and Gen arcs, discussed in Chapter 13, and (ii) the fact that such arcs have replacers is predictable by law (see PN law 107 below). Hence, one can then apparently replace (125a, b) by the more accurate: (i) a. Noncopy Arc Cases of Successor(A j B) Either: (1) Erase (A, B), or (2) Not (Erase (A, B)) Λ (Marq arc (A) Ν Gen arc (A)) , (in which case, B is predictably erased by a closure replacer) , b. Copy Arc Cases of Successor(A 1 B) Not (Erase (A,B))ANot(Marq arc(A)vGen arc (A)). Hence, it is still unnecessary for particular rules involving successors to distin­ guish copy from noncopy cases other than by specifying whether the successor erases the predecessor.

11.8. COREFERENTIAL ARCS AND COPY ARCS

519

Thus, in present terms, even though copy structures involve distinct arcs from the successor and its predecessor, the rules determining these need not refer to the third arcs in question. This result is only possible because The Replacer Erase Law is unconditional. If the other alterna­ tive had been adopted and The Successor Erase Law had been made un­ conditional, (125) would not be true, and there would be no general way for individual languages to distinguish copy from noncopy successor/ predecessor structures without reference to copy arcs themselves. 11.9. Constraints on internal survivors There are, within the TG literature, studies which attempt to account for various pronominalization facts by appeal to the principle of the trans­ formational cycle. Ross's(1967b) analysis is among the best known and most interesting of these. Although the present framework, of course, makes no use of any notion like the transformational cycle, nor would such use even be coherent in APG terms, 22 there is an important grain of truth in these TG studies. There is a single principle governing anaphoric connections which underlies a majority of the observations which have led to claims that such and such pronominalization rule or condition is cyclic. Our goal in this section is to explicate this claim by formulating a PN law which has the relevant facts as consequences. The principle in question bears on the previously touched on question of the number of possible sur­ vivors of a clan. Earlier, we considered principles guaranteeing in a range of cases that clans have at least one survivor. In this section, it will be a matter of principles guaranteeing that clans have no more than one survivor.

We first explore the possible relations between D-overlapping struc­ tural arcs, that is pairs of arcs satisfying:

This follows since the cycle presupposes a notion of rules mapping struc­ tures into other structures, hence of rules applying, hence it making sense for one rule to apply before another. None of these presupposed conditions holds in APG terms.

11. REPLACERS AND ANAPHORA

520

(126) Structural (Α Λ B) A D-Overlap(A, B) . Since this combination will be referred to frequently, we introduce more compact terminology:

(127) Def. 191: T w i n s ( A l B ) «-> Structural (AAB) Λ D-Overlap(A, B). Thus, twins are distinct overlapping structural arcs. Successor/Predeces­ sor pairs are twins, as are the kind of self-sponsoring arcs we have taken to reconstruct "coreference." The first question we consider is the possible "sources" for twins. Recall the notion Entrant. An entrant is an arc without a predecessor. There are two types of entrants, self-sponsoring arcs and grafts. We prove the stronger result that nonself-sponsoting entrants and grafts are coextensive: (128) THEOREM 117 (The Nonself-Sponsoring Entrant Theorem) Erttrant(A) A Not(SeIf-Sponsor( A)) G r a f t ( A ) . P r o o f . Consider the implication from left to right. Let A' be a nonself-

sponsoring entrant. If, contrary to the consequent, A' is an organic arc, then, since it does not sponsor itself, it has a distinct sponsor, and a D-overlapping sponsor, i.e., by definition, a predecessor, contradicting the fact that it is an entrant. From right to left, one can reason as follows. If A' is a graft, it cannot be self-sponsoring, for this would make it organic. Moreover, grafts cannot have predecessors for these are overlapping spon­ sors. Hence A' is an entrant. QED. Next, we show that twins which are both entrants are self-sponsoring: (129) THEOREM 118 (The Twin Entrant Theorem) T w i n s ( A 1 B ) Λ Eniranf (AAB) -> SeZf-Sponsor (AAB). P r o o f . Let A' and B' be twins such that both are entrants. It follows

from Theorem 117 that if the consequent is false, A' and B' are grafts. Therefore, the theorem is proved by showing that the grafthood of A' and B' yields a contradiction. Consider PN law 13:

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

521

(i) PN Law 13 (The Graft Overlap Law) Graft(A) AOverlap (Α,Β) Λ Structural (Α Λ B) -> R-Successor(B j A). (i) entails that if A' is a graft, B' is an R-successor of A'. But since A'^ B', this means that B' is either a successor of A' or an R-successor of a successor of A'. Hence, B' is a successor, contra­ dicting the assumption that it is an entrant. QED. Incidentally, it follows also that distinct structural grafts cannot overlap, that is, that both members of a twin pair can never be grafts: (130) THEOREM 119 (The Graft Nontwin Theorem) Grafi(AAB) -> Not(Twins( A, B)). Proof. Let A' and B' be grafts. If, contrary to the theorem, A' and B'

are twins, then they are structural and overlap. It then follows from The Graft Overlap Law, that R-successor (A', B') and R-successor (B', A'). This is only possible if A' = B', contradicting the D-overlap part of the definition of "Twins." QED. Next, it is obvious that if two arcs are twins and not both entrants, then the nonentrant(s) are successors: (131) THEOREM 120 (The Nonentrant Twin Theorem) Twins( A, B ) a Not (Entrant {A)) -> (3C)(Successor(A, C)) . Proof. Immediate from the definition of "Entrant." QED.

We can now prove the following, which characterizes the nature of twins which are not both self-sponsoring: (132) THEOREM 121 (The Twin Characterization Theorem) Twins(A l B) A Not(SeIf~Sponsor(A Λ B)) -» (3C) (Successor(A ,C) ν

Successor (Β,C)) . Proof. Let A' and B' be twins not both of which are self-sponsoring.

There are several possibilities. Case a. A' and B' are both entrants. But Theorem 118 would then re­ quire that both be self-sponsoring, contradicting the antecedent.

522

11. REPLACERS AND ANAPHORA

Case b. Without loss of generality, suppose that B' is an entrant and A' is not. Then the consequent follows immediately from Theorem 120. Case c. Neither A' nor B' is an entrant. The consequent again follows immediately from Theorem 120. QED. The upshot of these theorems is the following. There are, as informal­ ly claimed earlier at several points, only two "sources" for twins. One "source" is the possibility of twin arcs both of which are self-sponsoring. The other is the possibility of successors. These "sources" yield all and only the following kinds of twin pair: (133) Twin Pair Types If Twins(A 1 B) then either: a. Entrant(AAB). Therefore j Self-Sponsor(AAB), via Theorem 118, or b. Entrant(B)ANot(Entrant(A)) 1 Therefore, via Theorem 120: (i) (3C) (Successor (A,C) . Therefore, either: R-Successor (Α,Β), or: (ii) (3D)(Entrant(D)ATwins(B,D)AR-Successor(A,D)), or: c. Not (Entrant (A ν B)). Therefore, either: (i) Linked-R-Successor(Α,Β) or: (ii) (3E) (3G) (Entrant (E A G) A Twins (E,G) A R-Successor (A,E)

A

R-Successor (B,G). Necessarily Self-Sponsor(EAG). We can make this discussion slightly clearer by introducing further terminology. We define the notion Lineage, a set of arcs containing all and only an entrant arc and its R-successors: (134) Def. 192: Let X be a set of arcs. Then: Lineage(X) *-* ((3B) (Entrant (B) A B e X A (VA) (A eX *-»

R-Successor (Α,Β))). There are thus two types of lineages, those whose defining entrants are self-sponsoring, 23 and those whose defining entrants are grafts. Recalling 23

Members of these lineages are members of primal clans. We could easily then define the notion Primal Lineage. It would perhaps make more sense to de-

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

523

the notion Clan, there is an obvious relation between clans and lineages. Every clan is a set of one or more lineages composed of overlapping arcs. It follows from Theorem 117 that a clan containing a lineage whose entrant is a graft can contain only that lineage. Lineages with graft entrants de­ fine unilineage clans. On the other hand, lineages with self-sponsoring entrants can, but need not be, in clans containing 2 to η lineages, since we have imposed no constraint on the number of self-sponsoring arcs which can overlap. Unlike the arcs in a clan, all arcs in a lineage are ordered by the Suc­ cessor relation. They form a sequence or chain with 1 to η members, the first member being the entrant, the second its successor if any, the third the successor of the successor of the entrant, if any, etc. It is useful to have a term for the opposite of an entrant, that is, for the last member of a chain formed by a lineage; (135) Def. 193: Egresser(A) *-» Not((3B)(Successor(B, A))). Hence, a lineage consists of a sequence of arcs whose first member is an entrant and whose last member is an egresser. Lineages determined by entrants without successors each consist of a single arc which is both an entrant and an egresser. It is also useful to have terminology which permits, for any arc, A , reference to the entrant arc which is the first arc in the sequence defined by the lineage containing A , or to the egresser arc which is the last arc in the sequence. Hence: (136) Def. 194: Ur-Predecessor(A,B) «-» R-Predecessor(A1B)AEntrant(A). (137) Def. 195: Ur-Successor (A,B) R-Successor (Α,Β) Λ Egresser (A). Every lineage contains an arc which is the Ur-Predecessor of every arc in that lineage, and an arc which is the Ur-Successor of every arc in that fine "Primal Clan" in terms of primal lineage, rather than directly, as in (11.101) above.

524

11. REPLACERS AND ANAPHORA

lineage. Unilineage clans contain one Ur-Predecessor, multilineage clans many. The twin pair analysis in (133) now amounts to this. Arcs can be twins, as in (133a), even though they are in different lineages, either by both being self-sponsoring, or by being R-successors of entrants of dis­ tinct lineages, necessarily then lineages with self-sponsoring entrants. Or, arcs can be twins simply by being members of the same lineage, and hence being linked by R-Successor. Recall The S-Graph SS Condition (4.29e), which requires that the set of structural arcs of a Surface Sentence (SS) form a tree. Since a tree is a connected graph without cycles, this means, in effect, that SSs can con­ tain neither twins nor circuits. Absence of surface twins is a necessary though not sufficient condition for treehood (see note 7 of Chapter 4). Thus, given (4.29e), languages must contain devices guaranteeing that SSs do not contain twins. One can see this as the motivation for phenom­ ena like equi (i.e., unhooking overlapping arcs which are not successor and predecessor) and for coreferential arcs, for both of these serve to eliminate twin pairs. It can also be seen, at a more abstract level, as a motivation for The Replacer Erase Law and The Successor Erase Law. For the latter eliminates twins from S-graphs in all cases and the former in all cases where the cosponsors of a replacer overlap. The motivation for banning twins from SSs is not a priori clear. It is not self-evident why natural languages are such that this condition holds. One can conjecture that it has to do with the efficiency of speech recog­ nition and parsing mechanisms, which are better off if tree conditions and hence twin exclusion holds. 24 The question should be raised whether The S-Graph SS Condition, stated here as an independent principle of APG, is not a theorem of other 24 It is, of course, not difficult to understand why overlapping arcs exist. Selfsponsoring twins permit logical forms in which a single element figures as argu­ ment in more than one propositional form. Twins which are members of the same lineage are an immediate consequence of successorhood.

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

525

independent assumptions. Our first reason for suspecting this is that part of what this condition guarantees is already assured independently of (4.29e). The nonexistence of SS twins is already a provable consequence where Twins (A, B) and Linked-R-Successor (A, B). That is, it is assured where A and B are members of the same lineage: (138) THEOREM 122 (The Linked-R-Successor Surface Arc Theorem) T w i n s ( A l B ) ALirtked-R-Successor(A t B) -* Not(Suriace A tc( A a B ) ) . Proof. Let A' and B' be Linked-R-Successor twins. Assume without

loss of generality that: (i) Surface arc (A')

Λ

R-Successor (A', B').

Therefore, since A'^ B' by the definition of "Twins", it follows that: (ii) (3C) (Successor (C, B'). Let C' be the successor of B'. There are now two possibilities. Either B' has a replacer or not. If it has a replacer, it is erased by that replacer according to The Replacer Erase Law, and is then not a surface arc. Or, B' does not have a replacer, in which case it is erased by C', via The

Successor Erase Law, and is not a surface arc. Hence, at least one of A' and B' cannot be a surface arc. QED. Thus, to an extent represented by Theorem 122, the S-Graph SS C ndition already says more than is necessary. However, in cases of twins that are not members of the same lineage, nothing in previous assumptions in­ dependent of The S-Graph SS Condition guarantees that at least one of a twin pair is not a surface arc. However, we now develop a new PN law which does guarantee this result, as well as a number of more restrictive consequences for pronominalization phenomena of a possibly surprising character. Therefore, given Theorem 122 and this new law, much of what The S-Graph SS Condition says is independently guaranteed. This sug­ gests that in a proper theory, this condition will actually be a theorem. However, we have not yet been able to prove it because we have not proved, even with the new law just mentioned, that it is impossible for SSs to contain circuits. Thus, we have decided to leave (4.29e) as is,

526

11. REPLACERS AND ANAPHORA

for the moment, although strictly speaking we could, without loss of de­ sired consequences, replace it by a weaker condition requiring that SSs not contain circuits. We turn to the law which guarantees the nonexistence of any SS twins. Recall the notion Survivor, which refers to arcs without assassins, i.e., surface arcs or arcs which self-erase. We now want to define a more re­ strictive, though related notion, which permits us to say that an arc is a "survivor with respect to a certain constituent." By this, we mean that the arc in question is a member of that constituent and has no assassin which is a justified member of that constituent, although it may have an assassin which is not such a member. (139) Def. 196: Let Z be a set of arcs and X a constituent of Z with some endpoint in Z as point (see (7.1)). Then: Internal Survivor(A 1 X) *-* Not((3B)(BeX Λ Assassinate(B 1 A) Λ

(VC)(Sponsor(C,Β) -CfX))). (139) makes use of the fact that constituents are R-graphs and hence sets of arcs. Thus an arc, A , is an internal survivor of a constituent X if and only if A is a member of X and there is no member of X , B , such that B assassinates A and all of B's sponsors are members of X. We now claim a fundamental constraint on overlapping structural arcs can be expressed in terms of Internal Survivor: (140) PN Law 94 (The Internal Survivor Law) Internal Survivor(A j X)Alnternal Survivor(B,X) - Not (Twins (A,B)) . Evidently, this law guarantees that no well-formed SS can contain a twins pair. This follows since SSs are constituents, and if neither member of a pair of twins is erased (a necessary condition for being in an SS), then both are internal survivors of that SS. The latter follows since if an arc is not erased, it is not assassinated, and if it is not assassinated, it is not assassinated by the kind of arc mentioned in the definition of "Internal Survivor."

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

527

PN law 94 may be stronger than ultimately necessary in certain re­ spects since Theorem 122 guarantees that SSs never contain twins which are related by R-successor, that is, which are members of the same line­ age. And Theorem 122 was proved independently of The Internal Survivor Law. However, the latter law generalizes far beyond the domain of SSs to all constituents and thus would only be excessively strong vis-a-vis those twins which are members of the same lineage if one could prove: (141) Linked-R-Successor (A,B) ATwins (A1B) Alnternal Survivor(A.X) -» Not (Internal Survivor(BjX)). However, we have not proved (141) independently of The Internal Survivor Law and doubt that is provable without this constraint. Hence, at the moment, one could not in general weaken (140) by limiting it exclusively to those twin pair members which are not lineage mates. We earlier considered cases such as (42), where all members of clans were erased, and considered constraints blocking this in a wide range of cases. The most obvious consequences of PN law 94 are relevant to the opposite situation, where more than one member of a clan fails to be assassinated. This is now precluded. Consider structures like: (142) a.

Mary

tickled

b.

Joe

stngs

528

11. REPLACERS AND ANAPHORA

® I Joe

(by) Louise

(was) described

All examples like (142), in which twins ate both not assassinated, are now ill-formed. In (142a) A and B are internal survivors of the constit­ uent corresponding to A's tail. These cases involve exclusively selfsponsoring arcs. However, in (142c), A and C are internal survivors of the constituent corresponding to their tail, and only C is self-sponsoring. In still other cases, PN law 94 will block situations in which neither arc is self-sponsoring. One example is:

(was) told

(hod) (been) elected

UN Joe

UN

Here A and D , both of which are successors, are internal survivors of the constituent corresponding to the tail of A .

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

529

In all these cases, the consequences of The Internal Survivor Law are straightforward and evidently desirable, under the assumption that SSs meet tree conditions. However, this law has far more interesting, because less immediately obvious, implications. Some of these relate to the assumptions of certain transformational studies that aspects of pronominalization are cyclical. We turn to these presently. One significant consequence of The Internal Survivor Law, which is far from obvious, is that self-erasure is limited in distribution in an un­ suspected way. Both members of a twin pair cannot self-erase: (144) THEOREM 123 (The Twins Multiple Self-Erasure Theorem) T w i n s ( A t B ) -+ N o t ( S e l f - E r a s e ( AAB)). Proof. Let A' and B' be twins, and assume, contrary to the theorem,

that both A' and B' self-erase. There is at least one constituent con­ taining both A' and B', namely, Q', the R-graph of the PN from which they are SAX. Since both A' and B' self-erase, neither can have an assassin without contradicting The Unique Eraser Law. Hence A' and B' are both internal survivors of Q', contradicting The Internal Survivor Law. QED. Theorem 123 means that there are no well-formed PN fragments of the form: (145)

A ond B structural

b •* Thus, regardless of whether A and B are neighbors or whether C exists, overlapping structural arcs like A and B cannot self-erase, given The Internal Survivor Law. The implication is that self-erasure cannot

11. REPLACERS AND ANAPHORA

530

contribute to satisfaction of the requirement that the structural arcs of SSs be trees. This implication is strengthened by the following: (146) THEOREM 124 (The Twins Self-Erasure Theorem) Twins(A l B) /\Self-Erase(A) -» (3C)(Assassinate (C,B)) . Proof. Let A' and B' be twins and assume A' self-erases. Assume the contrary of the theorem, hence B' has no assassin. There is, as in the previous theorem, necessarily one constituent containing both A' and B', namely, 0', the R-graph of the PN from which they are SAX. Now, since A' self-erases, it can have no assassin, and is hence an internal survivor of Q'. But since, by the contrary of the theorem, B' has no assassin, it is also an internal survivor of 0', contradicting The Internal Survivor Law. QED. Theorem 124 is an empirically important result, greatly limiting the possi­ ble analyses for a wide range of cases. Consider equi cases like (147a) which, in our terms, have PNs of the form in (147b): (147) a. Jack wants to sing. b.

Jack

(to) sing

wants

A priori, nothing precluded an alternative analysis for sentences like (147a) in which B self-erases instead of being erased by A . This would yield the same S-graph that (147b) yields. However, Theorem 124 shows that such an analysis is in general impossible. Hence, the Internal Sur­ vivor Law, via Theorem 124, contributes to eliminating multiple analyses. In cases like (147), the eliminated analysis seems clearly wrong. For to say that B self-erases is to suggest that A is irrelevant to the erasure.

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

531

But in general equi constructions are only possible when there are over­ lapping arcs. It is not in general possible to self-erase arbitrary 1 arcs. These only erase in contexts like (147). Hence, analyses of the type ex­ cluded by Theorem 124 are in general incorrect, supporting this theorem and The Internal Survivor Law. In Chapter 9 we observed that although no constraints had been im­ posed on self-erasure, such limitations would no doubt ultimately prove rather significant. The result following from Theorem 124, which pre­ cludes self-erasure in contexts otherwise like (147), is consistent with a potential constraint blocking self-erasure of most types of Nominal arcs whose heads are members of Explicit. Such self-erasure might ultimately be limited to pronominal arcs (to handle cases like (3.11) above) and possibly a few others. We turn to implications of The Internal Survivor Law bearing on TG work claiming that aspects of pronominalization are cyclic. Involved here are nonobvious implications of PN law 94 greatly limiting the class of possible seconders for coreferential arcs (those for copy arcs are restricted without this to the successors of the arcs copy arcs replace). These im­ plications are related in part to the a priori mysterious final conjunct in the definition of "Internal Survivor", which we will explicate. If one considers structures like (2) above, repeated as (148), the only reasonable choice for a seconder of the coreferential arc is the overlapping arc not replaced: 25

^Ne use the weak locution "reasonable choice" because, as made clear in the discussion of the undefined concept Family in section 4, we have not formal­ ized any constraints on the nature of the cosponsors of (anaphoric) replacers. Strictly speaking, at the moment, nothing precludes the absurd possibility that, in (148), C could be seconded by the P arc D , or some branch of the 1 arc, A , etc. Perhaps some such possibilities could be excluded, in the absence of an ultimately desirable account of Family, by requiring that arcs in anaphoric chains be restricted, e.g., to Nominal arcs. We have not investigated this question.

532

11. REPLACERS AND ANAPHORA

(148)

Mary herself

praised

However, when clauses like (148) are embedded, it would a priori become possible for the seconder to be, e.g., a distinct overlapping arc in a high­ er structure. Consider: 100

(149)

thinks

praises she

herself

In (149), the three anaphoric arcs G , H , and I do not have their second­ ers indicated. Since (149) should give rise to: (150) Mary says she thinks she praised herself. we would like the seconding pairs to be: (151) a. Seconds(C, I). b. Seconds(B 1 H). c. Seconds (A, G). This would guarantee that H arc antecedes I, that G arc antecedes H, and that A arc antecedes G, which seems correct.

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

533

While certain combinations of seconders with the replacers in (149) are already blocked by The Anaphoric Chain Law and its consequences, e.g., having G, H, and I seconded by some combination of B, C, and D , other possibilities distinct from (151) are not precluded in this way. It is notable that (151) has a "cyclic" character in the following sense. Each anaphoric arc in (151) has as seconder an arc which is maximally "close" in terms of superordinate structures. Hence, I has a local seconder, H has a seconder in the immediate higher clause, as does G . Compare this with the following "unnatural" seconding pattern: (152) a. Seconds (Β, I). b. Seconds (B, H). c. Seconds(A 1 G). (152) is not precluded by The Anaphoric Chain Law. However, interesting­ ly, it is precluded by The Internal Survivor Law, while (151) is not. The problem with (152) is the seconding of I by B . Forthissecondingyields a violation of The Internal Survivor Law. Let us consider why. C and D are arcs internal to the constituent with point 300. Therefore, to remain consistent with PN law 94, C and D must not be internal survivors of the constituent defined by 300. However, under (152), they are. For, although both C and D are locally erased (by their respective anaphoric replacements H and I, under (152), H and I are both seconded by B . Hence, their sponsors are not both inter­ nal to the constituent defined by node 300, as required in the definition of "Internal Survivor." Therefore, both C and D are internal survivors of that constituent. On the other hand, in what we take to be the correct analysis of (150), (149), the seconder of I is C (exactly parallel to the situation in (148)), and both sponsors of D's assassin are internal to the 300 constituent. The Internal Survivor Law both eliminates certain a priori possible seconding patterns and guarantees that the seconding pattern obtainable

534

11. REPLACERS AND ANAPHORA

when clauses like (148) are embedded is, with respect to the invariant arcs, identical to that of nonembedded cases. That is, (152) has, from the point of view of (148), an "unmotivated" seconding of I by an exter­ nal arc when there is a local arc capable of serving as seconder. With respect to (149), the same considerations preclude a seconding pattern of the form: (153) a. Seconds(C 1 I). b. Seconds (A, H). c. Seconds (A, G). Here B and C would both be internal survivors of a constituent, that defined by node 200. This follows since their assassins, respectively G and H , would only have both their sponsors internal to the constituent defined by 100, while B and C are internal survivors of 200. Next, we show how considerations of the sort just gone over have as consequences facts often described in terms of a cycle in TG terms, namely, the interaction of English reflexivization with raising structures. Crucial to these arguments is the assumption, probably not correct, that reflexivization is governed by a clause mate condition. 26 The facts are then that (i) raising feeds reflexivization with respect to a main clause (see (154)); (ii) does not bleed reflexivization with respect to complement clauses (see (155)), and (iii) there are cases where reflexivization must occur in "sandwich" fashion, that is, raising must first create the condi­ tions in a main clause for reflexivization and then the antecedent is raised into a still higher clause {see (156)), yielding in TG terms a rule ordering sequence Raising-Reflexivization-Raising: (154) a. I tickle myself (*me). b. I believe (that) I (*myself) tickle myself. c. I believe myself (*me, *1) to tickle myself.

2 6 Recent counterevidence to this claim includes sentences like (i) cited in Bresnan (1976): (i) I don't want myself getting left with all of the work.

535

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

(155) a. They believe (that) I tickle myself (*me). b. They believe me to tickle myself (*me). (156) Joe believes himself to have proved himself innocent. Sentences like (156) give, at first glance, strong arguments for the cyclicity of reflexivization (see Postal [1974a: chapter 8, section 2], and Keyser and Postal [1976: chapter 29]) since apparently the pronoun must raise into the prove clause, triggering reflexivization, before the subject raises out of the prove clause.

However, the facts noted are basically consequences of The Internal Survivor Law and the following independently needed generalization about English pronouns (i.e., needed for simple clauses like (154a)): (157) When the head of a 1 arc pronominally antecedes the head of a neighboring 2 arc, the head of the latter must correspond to a

nominal of the form X-se/f. The Internal Survivor Law entails that the successor arcs associated with raising cannot bleed the choice of self. Consider (156), which would have, in our terms, the PN: (158) believes

(foMhave) proved

innocent

himself

himself

536

11. REPLACERS AND ANAPHORA

The key question is why the pronoun heading arcs H and M is himself and not him. The answer is the same as the reason why the pronoun head­ ing G and K is himself and not him. In both cases, the pronoun heads a 2 arc and is pronominally anteceded by the head of a neighboring 1 arc. In the case of the rightmost himself, H is arc anteceded by G (the anaphoric replacement of H's seconder, B). But G and M (the succes­ sor of H due to raising) are neighboring 1 and 2 arcs, and the head of H is the head of L . Hence, generalization (157) requires that the head of M have the form X-self. G is arc anteceded by A, its pure seconder. A and K (G's successor) are neighboring 1 and 2 arcs. Hence, the head of A pronominally antecedes the head of G , which is also the head of K , and the latter must have the form X-self, according to (157). Crucial in this explanation is the notion Pronominally Antecedes, defined earlier in terms of Arc Antecedes, and the fact that successors and their predeces­ sors overlap. But The Internal Survivor Law is also needed. For it is this which re­ quires that H be seconded by B and not by A . The latter seconding would mean, inter alia, that condition (157) would not hold for the head of H , and the reflexive form of the latter would be unmotivated. More general­ ly, The Internal Survivor Law means that foreign successors like those associated with raising will never effect pronominalization possibilities for arcs seconded by the predecessor of the raising successor. In this respect, The Internal Survivor Law strengthens some implica­ tions already deducible from PN law 91, The Inherent Anaphoric Arc Seconder Law, which requires that the seconders of inherent anaphoric arcs (hence coreferential arcs) be self-sponsoring. This already precludes, independently of The Internal Survivor Law, PNs like (159b) for raising sentences like (159a):

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

537

(159) a. I believe Joe to tickle himself, b.

believe

himself

tickle

(159b) does contradict The Internal Survivor Law, since both B and C are internal survivors of the complement constituent. However, (159b) also violates The Inherent Anaphoric Arc Seconder Law, since the second­ er of D is A, a successor, which is not, as required, self-sponsoring. Next, we show how The Internal Survivor Law has as a consequence the distribution of facts which led Ross (1967b) to conclude that English pronominalization was cyclic. Ross's major observation of relevance was the contrast between pairs like: (160) a. Finding out he had cancer worried Ted. b. Finding out Ted had cancer worried him. In (160a), Aeand Ted can be "««referential," while this is not possible for Ted and him in (160b). The important aspect of sentences like (160) is that they involve, independently of pronouns, an unhooking pattern, illustrated by (161b) for the simpler example in (161a): (161) a. Finding out things worries Ted. b.

finding out

things

Ted

worries

538

1 1 . R E P L A C E R S AND A N A P H O R A

The upstairs 2 arc unhooks the downstairs 1 arc. The question is why this unhooking pattern can interact with pronouns to yield (160a) but not (160b). The answer is The Internal Survivor Law, as made evident by the needed structure for (160b), which would be:

(162) worried

100

Ted

had

him

cancer

Here the unhooking pattern is identical to that in (161b). The difference is that Ted also heads a complement clause arc and that A and B cosponsor a coreferential arc, D. (162) yields (160b), as desired. However, this structure cannot be well formed because it contradicts The Internal Survivor Law. For A and C are twins, and yet both are internal survi­ vors of the constituent whose point is node 100. C is an internal survi­ vor of this constituent because it has no assassin at all. A is an internal survivor of the same constituent because it has an assassin external to that constituent, namely, B . (162) should be compared with (163), which yields the well-formed (160a) (163) 100 worried

finding out hod

cancer Ted

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

539

Here, in contrast to (162), only A is an internal survivor of the constitu­ ent corresponding to node 100. C is not, since it is assassinated by D , and both of D's sponsors are internal to the 100 constituent. Hence, The Internal Survivor Law makes exactly the required distinction between (160a, b), interacting perfectly with other assumptions. We hope to have shown how this law does a considerable portion of the work which has, in the recent past, been attributed in TG oriented studies to the fact that pronominalization is in some sense cyclic. In our terms, this previous assumption contains the following core of truth. The Internal Survivor Law guarantees that, with respect to twin pairs, each constituent is by itself suitable, at least with respect to tree conditions on sets of structural arcs, for being an S-graph constituent, independently of any structure outside of that constituent. It does this by requiring that every twin pair internal to any constituent X be such that at least one member is assassinated by an arc, A , which is (i) internal to X and (ii) such that all of A's sponsors are internal to X . The latter requirement is natural in the sense that it reconstructs the notion that the assassina­ tion must be "justified" internal to X, and therefore only possible if the assassin itself would "justifiably" exist internal to X. And, in our terms, "justifiable" existence for an arc in X means having the neces­ sary and sufficient sponsors in X . Formally, the requirement that all of the sponsors of an assassin rele­ vant for survivorhood internal to a constituent X be internal to X is necessary in our terms because of anaphoric arcs. Since these are replacers, it follows (from The Replacer Erase Law) that every arc with an anaphoric replacement is not only assassinated but locally assassinated, and hence, has an assassin internal to every constituent containing it. Hence, if, as is obvious, we want some arcs with anaphoric replacers nonetheless to violate internal survivor conditions (see, e.g., some of the analyses above of (149)), we need a stronger condition. This must be of the sort provided by The Internal Survivor Law based, as it is, on a defi­ nition of "Internal Survivor" sensitive to the locus of the sponsors of assassins.

540

11. REPLACERS AND ANAPHORA

To conclude this discussion of how The Internal Survivor Law recon­ structs or explains many facts considered to devolve upon the notion of a cycle, observe that some such facts in the general area of anaphora and "coreference" follow from deeper aspects of APG. Consider in this re­ gard stacked equi examples like: (164) Melvin expects to want to win. In a TG framework, a major problem is what prevents application of Equi from applying first at the highest level, deleting the antecedent for appli­ cation at the lowest level (see Keyser and Postal [1976: chapter 29]). Of course, this problem depends on the assumption that Equi only applies between main and immediately subordinate complements, and is partially solved by the claim that Equi is cyclic. We say "partially" because the account remains as ad hoc as any arbitrary rule ordering solution, in the absence of a principle of universal grammar which requires that Equi be cyclic. In APG terms, (164) has nothing to do with The Internal Survivor Law but illustrates that without ad hoc rules there is no way that the erasure of one arc by a "higher" arc can "bleed" the ability of the erased arc to serve as an eraser. In APG terms, the structure of (164) is:

expects

(to) want Melvin

(to) win

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

541

The fact that A erases B is irrelevant to the fact that B erases C . The former in no way impedes the latter. There is no need for a special principle to prevent one instance of Equi from bleeding the other. This is a consequence of the APG assumption that sentences are reconstructible in terms of PNs. One further matter worth touching on may be related to The Internal Survivor Law. Consider an example like: (166) Joe believes himself to sing. We would like such sentences to only have PNs in which the pronoun him­ self corresponds to the head of a coreferential arc and to the immigrant

arc successor of that anaphoric arc. However, a priori , it would be con­ ceivable for (166) to have a structure of the form: (167)

believes

himself

Joe

Peculiar in this structure is that the complement arc's (C) foreign suc­ cessor (B) is parallel to a distinct arc (A) . The replacer D is then cosponsored by two main clause arcs, A and B , and is itself a main clause arc. The form himself is exclusively a main clause constituent. Compare this to what we take to be the proper analysis:

542

11. REPLACERS AND ANAPHORA

(168)

believes

himself

In (168) the replacer, D , is a complement clause arc and has a main clause successor. So the pronominalization in (168) is identical to the pronominalization in a structure with no raising. But not so in (167). That (167) is ill-formed follows from PN law 90, The Coreferential Arc Law. This says that a coreferential arc must replace an arc whose only coordinate is C 1 . D in (167) is a coreferential arc, since it is a kernel anaphoric arc, and not a copy arc. However, D replaces B , an immigrant arc, which hence cannot have coordinate C 1 at all. The connection between structures like (167) and The Internal Survivor Law is the following. The Coreferential Arc Law guarantees that the twins pair created by permitting an immigrant arc to be parallel to a selfsponsoring arc (B to be parallel to A in (167)) which are not related by R-successor cannot always be eliminated by the device of coreferential arcs. For example, D is impermissible in (167). Other patterns of coreferential elimination of twins, e.g., having D replace A and be second­ ed by B, would certainly violate "pronominalization constraints" and in many cases, other laws. For instance, the replace pattern just described would violate PN law 91, The Inherent Anaphoric Arc Seconder Law, which requires the seconder of an inherent anaphoric arc to be selfsponsoring (B in (167) is not self-sponsoring and thus could not second a coreferential replacer of A). Although we have not accomplished this,

11.9. CONSTRAINTS ON INTERNAL SURVIVORS

543

one can then possibly prove that a twin pair (A, B) containing an immigrant arc A whose members are not lineage mates but are parallel is such that neither can be replaced by a coreferential arc. However, we know from The Internal Survivor Law that at least one of such a pair must be erased. This raises the question of how. Even more significantly, we know that neither member of such a pair can erase the other, for this follows directly from PN law 11, The Parallel Assassin Law, discussed in Chapter 5, which allows parallel assassinations only if the assassin is the successor of the erased arc. Consequently, in cases otherwise like (167), A and B cannot be in an unhooking pair. This means that the standard mechanisms which serve to eliminate twin pairs are not capable of eliminating twin pairs like that in (167). The upshot of the discussion is this. Given The Internal Survivor Law, plus further reasonable constraints on zeroing and unhooking, it should ultimately be possible to prove the following:

(169) CONJECTURED THEOREM Immigrarit(A) A P a r a i I e l ( A l B ) -» R - L o c a l S a c c e s s o r ( B t A ) .

The logic of the proof would be this. Independent considerations prevent, as already partially sketched, the assassination of either member of a twin pair instantiating the antecedent of (169). However, The Internal Survivor Law, mandates the assassination of one of them. (169) would be an important result. It would mean, informally, that it is impossible to "raise" an element into a constituent already containing it, as in (167). It would thus serve to greatly restrict possible analyses of immigrant situa­ tions. We are convinced that (169) is true. If it proves not to be a theorem, we would take this as grounds for stipulating it as a PN law. The principle in (169) is related to another important claim, namely: (170) Overrun (A,B)

Not (Overlap (A,B)) .

Overrunning arcs cannot overlap the arcs they overrun. We are convinced that (170) is true, knowing of no cases which contradict it. However, we

544

11. REPLACERS AND ANAPHORA

have not been able to prove it. If (170) is provable, this can apparently only be the case if (169) holds. For one special case of what (170) pre­ cludes is a situation where one arc, B , is overrun by a parallel immigrant arc, A . But overrunning in this class of cases would be precluded by (169), since it would require that B be an R-successor of A , and hence, if not A , either a successor of A or a successor of a successor of A , etc. Thus, it would be impossible for A's first coordinate index to be +1 of any coordinate index of B , as required by the definition of "Overrun." (170) should then be studied in context with (169). For it is likely that guaranteeing the truth of the former will be necessary, and, conceivably, even sufficient (given other current PN laws), to prove the latter. Finally, (169) will probably also be important in proving another prin­ ciple we take to be a truth of APG. This would preclude situations of the form: (171)

b

In (171) A , B , and C are all related by R-successor, that is, are mem­ bers of a single lineage. However, while A and C are parallel, B is parallel to neither. What is bizarre about such structures is that the nonparallel arc B has a predecessor and a successor which are parallel to each other, but not to it. Again, structures like (171) contradict (169) since C is an immigrant arc, and is parallel to A , but A is not an R-Iocal successor of C . More generally, (171) is a special case of situa­ tions characterizable as follows. (171) involves a set of arcs all linked by R-successor (that is, all lineage mates). Hence, they form a sequence ( ·•· A, B, C ·••) in which some members are neighbors and some not. This

X 1.9. CONSTRAINTS ON INTERNAL SURVIVORS

545

is itself not unusual. What is bizarre about (171) is that in the sequence there are neighbors "on both sides of" a nonneighbor, contradicting what we claim is a truth about APG: (172) R-Successor(CjA) ANeighbor(A1C) λR-Successor (B,A) a Not (Neighbor (A1B)) -» K-Successor (B1C). In other words, if B is an R-successor of one of two nonneighboring parallel arcs (A,C) linked by R-Successor, then B is also an R-successor of the other. Thus, a nonneighbor cannot be intermediate between two neighbors in a lineage. Again, we have not proved (172) and a proof is obviously connected to that of (169). Observe how (171) is inconsistent with (169). We conclude that (169) is rather central to proving a range of what appear to be basic truths about the system under development. 11.10. Appendix: ghost arcs and pro arcs In Chapter 10 we observed similarities between dummy nominals and anaphoric nominals and raised the question of a basis for this. The simi­ larity so far in APG terms is that dummy nominals and anaphoric nominals both correspond to the heads of Nominal arc grafts. We know that anapho­ ric nominals are the heads of pro arcs. We now show that ghost arcs are pro arcs, and hence extend the similarity provided by APG terms. Since a pro arc is by definition (see (11.15)) a Nominal arc graft not sponsored by a branch, and since a ghost arc is by definition a unisponsored Nominal arc graft, one can prove ghost arcs to be pro arcs if it is provable they are not sponsored by their branches: (173) THEOREM 125 (The Pro Archood of Ghost Arcs Theorem) Ghost arc (A) -» Pro arc (A) . Proof. Let A' be a ghost arc and let B' be its sponsor. Suppose the

contrary of the theorem. More precisely, since Nominal arc(A') and Graft (A'), suppose that: (i) Branch (B', A').

546

11. REPLACERS AND ANAPHORA

PN law 84, which we repeat: (ii)

PN Law 84 (The Ghost Arc Law)

Ghost(A)ASponsor(B j A) -> (3C)(R-Successor(C,A)AFacsimile(C,B)) entails that: (iii) (3C) (Facsimile (C, B') Λ R-Successor (G, A')). Let C' be an R-Successor of A' and a facsimile of B'. From the defini­ tion of "Facsimile": (iv) Neighbor (C', B') and hence: (v)

Tail(C) = Tail (B').

But, since R-Successor (C, A') : (vi) Head(C') = Head(A'). Since Branch (B', A') : (vii) Tail (B') = Head (A'). But (v), (vi), and (vii) determine that: (viii) Head(C) = Tail (C). That is, C' is a loop, contradicting Condition (2.52d), The No Loop Con­ dition, on R-graphs. QED. Hence, the present development guarantees that dummy nominals and anaphoric nominals both correspond to the heads of the limited set of arcs called pro arcs, a set with no other members. This provides an initial basis for the similarity between dummy and anaphoric nominals, although a great deal remains unaccounted for.

CHAPTER 12 LINEAR PRECEDENCE 12.1. lritroduc tory remarks That there is a relation of linear precedence in natural language is one point on which all linguists surely agree. But disagreements arise when it comes to specifying the nature and overall role of such a relation in linguistic theory. It is in a sense traditional to sharply differentiate linear precedence from so-called "grammatical relations," like subject, indirect object, modifier, etc. This distinction is codified in TG, where linear precedence forms one of the three primitive relations of sentence structure (along with labeling and constituency), while all other grammatical relations are either taken as defined, or rejected. Our own view of the role of linear precedence has undergone an extensive evolution in the course of develop­ ing the present work. We began by elaborating the claim of stage 2 RG that linear precedence is properly represented in terms of the same basic constructs as all other grammatical relations, that is, in terms of arcs. Without denying the many unique properties of linear precedence, this approach seems at first to deal in a methodologically desirable way with fundamental similarities between linear precedence and, e.g., subjecthood. For instance, it accounts for the fact that both involve binary, asymmetric, irreflexive relations between linguistic elements. Hence, our initial posi­ tion, one built into earlier chapters to greater or lesser degrees, was that there is a class of LP arcs, which are the basic molecules in the descrip­ tion of linear precedence phenomena. In sections 2 through 9 We present the rather elaborate theory of linear precedence ultimately developed on the basis of the view that there are

548

12. LINEAR PRECEDENCE

LP arcs. This conception originally seemed plausible, for one reason besides the parallelisms between linear precedence and other relations. Namely, since the number of distinct relations (and hence R-signs) recog­ nized in APG terms is relatively large, adding one more to account for linear precedence seems theoretically natural, as opposed to expanding some other aspect of the theory where the number of distinctions other­ wise necessary is quite small. However, in the course of developing an APG-internal conception of linear precedence based on the concept of LP arc, we gradually became convinced that this approach is fundamentally mistaken. Therefore, the account in sections 2 through 9 is one we no longer consider correct. After considerable hesitation, we have nonetheless decided to present it for the following reasons. While convinced that LP arcs do not exist, the account of linear precedence based on such arcs brings out in a novel and useful way important considerations relevant to any attempt to deal with linear precedence in APG terms. Thus, these sections should serve as a basis for future, more adequate developments (as well as providing some historical documentation of how initial APG work exploited ideas taken from RG and related work). A final reason for leaving the present incorrect account of linear pre­ cedence is that we have not yet had the opportunity to develop fully a more adequate account. In section 10, however, we consider in greater detail reasons for ultimately rejecting LP arcs and the account based on them. Section 11 expands this viewpoint in a different direction. As is evident from previous discussion, linear precedence plays a smaller role in APG, as in RG, than in other currently popular views of grammar. This is true regardless of the validity of LP arcs, etc. This restricted role of linear precedence correlates with the correspondingly greater role played by other relations, which is natural given the greater set of primitive relations recognized by APG. For example, in comparison to TG, APG descriptions involve linear precedence in only highly restrict­ ed aspects. Phenomena like passivization, raising, question formation,

12.1. INTRODUCTORY REMARKS

549

relativization, clausal extraposition, etc., have, as such, nothing to do with linear precedence. More precisely, APG claims that there is nothing in natural language corresponding to the movement rules of TG. This fol­ lows since there is no movement in APG descriptions, nor is it clear that there could be. From the APG point of view, theories like standard TG involve a massive exaggeration of the role of linear precedence in natural languages, an exaggeration based on a concomitant failure to perceive the role of a host of other relations. From an APG viewpoint, most TG descriptions involve an artificial attempt to describe phenomena not involving linear precedence by positing nonexistent linear precedence relations. Consider: (1) a. That Tricky is not in jail bothers Lucille. b. It bothers Lucille that Tricky is not in jail. In TG terms, examples like (lb) are normally described by positing a movement rule which repositions that complements to clause final position. This implicitly assumes that there is some sense in which the complement "once" linearly preceded the verb, the direct object, etc. There is no reason to believe this. In APG terms, (la) and (lb) share all initial gram­ matical relations and differ in that the former contains a ghost 1 arc, with the original 1 arc headed by the complement having a Cho arc local suc­ cessor. The fact that the complement is clause final is a function of the fact that those Cho arcs whose heads are linearly ordered generally deter­ mine a clause final ordering in English. Moreover, the class of Cho arcs, more generally, the class of arcs, whose heads can be ordered is deter­ mined by law (these must, with one exception, be heads of shallow colimbs [see below]). Similar remarks hold for passives, question formation constructions, relatives, etc. None of these involves statement of word order changes even in languages, like English, where they are correlated with distinct word orders. Expectably then, there are languages where, e.g., actives and passives do not differ in word order (see Perlmutter and Postal [1977]).

550

12. LINEAR PRECEDENCE

12.2. LP arc basics We build on RG and other work (see, e.g., Sanders [1967, 1970, 1972, 1975]), which concludes that linear precedence is basically a derivative or superficially determined aspect of grammar. We conclude that the dis­ tribution in PNs of those arcs which represent linear precedence (LP arcs) is largely governed by PN laws controlling the sponsors and erasers of LP arcs. These laws leave only a limited range of possibilities subject to individual language specification. The key aspect of these universal principles involves limits on the class of nonLP arcs whose heads can be connected by LP arcs (more precisely, whose heads can be the endpoints of LP arcs). We first introduce the notion LP-Connected, then review from Chapter 4 the notions Structural Govern and Quasi-Root, and define the notions Surface Structural Govern and Quasi-Rooted LP arc: (2) a. Def. 197: LP-Connected (a, b) «—• (3A) (LP arc (A) A Endpoints (a,b, A)). b. Def. 60: Structural Govern (a, b) «-» (3A)(Govern (a,b, Α) Λ Not (LP arc (A))). c. Def. 198: Surface Structural Govern(a,b) (ΉΑ) (Govern (a,b,A) a Not (LP arc (A)) a Surface arc (A)). d. Let X be a set of arcs. Then: i.

Def. 61: Quasi-Root (a,X) «-» Node Extractable (a,Χ) Λ Not ((3b) (Structural Govern (b,a))).

ii. Def. 199: Quasi-Rooted LParc (A) LP arc (A) Λ (Endpoint (b, A) A Quasi-Root (b,X)). The definition of "LP-Connected" in (2a) allows reference to nodes con­ nected by an LP arc independently of the "direction" of the arc, i.e., with no specification of which node is the head and which the tail. The definition of "Structural Govern" in (2b) refines the general notion Govern, introducing a relation that holds between two nodes just in case the R-Sign of the "connecting" arc is not LP. The definition of "Surface Structural Govern" in (2c) refines the notion Structural Govern, yielding a

12.2. LP ARC BASICS

551

relation that holds between two nodes in Structural Govern, provided the "connecting" arc is a surface arc. The definition of "Quasi-Root" in (2d) permits reference to a nonterminal node which is not structurally gov­ erned, although it may be governed. If a quasi-root is governed, the R-Sign of the arc it heads is necessarily LP. This follows immediately from the definition of "Structural Govern" referred to in Definition 61. A quasi-rooted LP arc is defined to be an LP arc with at least one endpoint which is a quasi-root. Quasi-rooted LP arcs currently play a very restrict­ ed role. We next introduce terminology permitting reference to different types of linear precedence apt to be confounded at an informal level of discourse: (3) a. Def. 200: LPs (a,b) «-• (3A)(LP arc (A) AHead (a,A) ATail (b,A)). b. Def. 201: Loose Precede (a, b) «-» (3c) (3d) (LPs (c,d) a R-govern (c,a) a R-govern (d,b)). In a large class of cases, Loose Precede provides an APG reconstruction of the informal, common linguistic usage of the term "precedes." 1 For instance, in John thought that Mary kissed the man in the blue collar, John loose precedes every other word in the sentence. Similarly, every word in the above italized sentence loose precedes every word to its right. LPs permits reference to a node a being the head of an LP arc with node b as tail without mentioning coordinates. In (4b), a partial PN for (4a) below: LPs (I, think); LPs ( think, 7); LPs (that, 8); LPs (John, saw); LPs (saw, Mary); LPs (Mary, 9); and LPs (in, Poughkeepsie): 2 (4) a. I think that John saw Mary in Poughkeepsie.

^One difference between Loose Precede and the pretheoretic notion Precede is that the former is not asymmetric but rather nonsymmetric. For example, in (13) below, node 9 loose precedes the node P-headed by John and conversely.

2In

(4b) and other PNs in this chapter, LP arc sponsors are often ignored. Also we commonly refer to nodes like John, eats, etc., as being LP-Connected, etc., instead of using more precise statements such as "nodes heading arcs P-headed by John," or "nodes corresponding to John," etc.

552

12. LINEAR PRECEDENCE

b.

6

LP I

think GR, LP •that

Loc

LP John

LP saw

LP Mary Marq LP Poughkeepsie

Each pair of nodes in (4b) which are in LPs are heads of neighboring

arcs. However, e .g., think does not LPs that and that does not LPs John, although in the surface string of (4a) there is a valid sense in which think precedes that and that precedes John. But think bears LPs to node 7, which R-governs that. Hence, Loose Precede ( think, that) by (3b). Simi­ larly, LPs ( that, 8) and R-govern (8, John). Thus, Loose Precede (that,

John). Moreover, Loose Precede (I, that); Loose Precede (I, John); Loose Precede (I, saw); Loose Precede (/, Mary); Loose Precede (I, 9); Loose Precede (I, in); Loose Precede (I, Poughkeepsie). This corresponds to the informal notion that I is the first word in sentence (4a). Finally, in all cases, if LPs(a,b) , then Loose Precede(a,b) . In (4b) it is no accident that the LP-Connected nodes are all and only the heads of neighboring arcs. The current claim is that there is only one

553

12.2. LP ARC BASICS

situation where nodes a, b are LP-Connected and not heads of neighbor­ ing arcs: where (i) a, b are both nonterminals and (ii) there is no node which structurally governs either a or h. This is precisely where a and b are quasi-roots. As mentioned in Chapter 4, this situation is ex­ emplified by "connected" discourse, as illustrated in (5a, b) below. (5) a. John entered the room at noon. He left at midnight. b. 7 LP

Temp

Temp

LP John

LP entered

LP (the) room LP

LP noon

LP

left Marq LP

12.3. Quasi-rooted LP arcs LP arcs are divisible into two exhaustive, disjoint groups: (i) selfsponsoring LP arcs with quasi-root endpoints and (ii) LP arcs which LP-Connect the heads of structural colimbs and which are sponsored by supports. One goal of this chapter is to impose PN laws which formally characterize the above division and the invariant properties associated with each subclass of LP arcs. We first turn to specifying which quasi-roots of a given R-graph are LP-Connected. For example, nodes 6 and 7 in (5b) are S-graph quasi-roots.

554

12. LINEAR PRECEDENCE

We view this as typical and assume that all S-graph quasi-roots are LP-Connected: (6) PN Law 95 (The Quasi-Root LP-Connectedness Law) Let SG be the S-graph of the R-graph of an arbitrary PN. Then: a -f= bAQuasi-Root(a,SG)AQuasi-Root(b,SG) -» LP-Connected(a,b). Thus, A in (5b) is lawfully determined. One must, however, impose further restrictions on quasi-rooted LP arcs, to insure that (i) if one endpoint of an LP arc is a quasi-root, then the other endpoint is also and (ii) if two nodes, a, b, are LP-Connected and a is an R-graph quasi-root, then both a and b are S-graph quasiroots. The first restriction prevents LP arcs, like A in (7a) below. The second restriction reflects the fact that S-graph quasi-roots are not neces­ sarily R-graph quasi-roots and vice versa, as illustrated in (7b), and the assumption that only S-graph quasi-roots need be LP-Connected. (7) a.

Jo runs

b. i. Melvin ate. Then he slept. 11.

eo

12.3. QUASI-ROOTED LP ARCS

555

In (7b, ii) both 15 and 60 are quasi-roots of the R-graph of (7b, ii) 3 But only 60 is a quasi-root of the S-graph associated with (7b, ii). Without a restriction that only S-graph quasi-roots are LP-Connected, B in (7b, ii) would be permitted, even though it appears useless. (Note that 19 is a quasi-root of the S-graph, but not of the R-graph, of (7b, ii), since it is the head of structural arc E . Hence, the LP-Connection of 19 and 60, via A , is correct.) To achieve these results we impose: (8) PN Law 96 (The LP Arc

Qiiasi-Root

Law)

Let SG be the S-graph of the R-graph of an arbitrary PN. Then: LP-Connected(a,b)AQuasi-Root(a,SG) -» Quasi-Root(b,SG). PN law 96 says that if two nodes are LP-Connected and one is an S-graph quasi-root, then the other is also. This blocks (7a), since LP arc A LP-Connects one S-graph quasi-root, 52, and a nonquasi-root, the node corresponding to slept. (7b, ii) is also blocked by PN law 96, since LP arc B connects an S-graph quasi-root, 60, with a nonS-graph quasi-root, 15. PN laws 95 and 96 do not complete the formal reconstruction of the in­ formal division of LP arcs presented above. One feature missing is a specification of sponsors for quasi-rooted LP arcs. We wish to insure that the class of self-sponsoring LP arcs is coextensive with the class of S-graph quasi-rooted LP arcs. Therefore, we insure that an LP arc is self-sponsoring if and only if its head (and consequently, via PN law 96, its tail) is an S-graph quasi-root: (9) PN Law 97 (The Self-Sponsoring LP Arc Quasi-Root Law) Let SG be the S-graph of the R-graph of an arbitrary PN. Then: LP arc (A)

3

Λ

AeSG -> (Self-Sponsor (A) «-» Quasi-Root (Head (A), SG)).

We have a r b i t r a r i l y represented D, E, and G as self-erasing in (7b, ii). We have not investigated the question of their proper erasers, which is irrelevant to the point at issue.

556

12. LINEAR PRECEDENCE

PN law 97 insures that in well-formed PNs, LP arcs like A in (5b) are self-sponsoring. 4 12.4. D-sponsored LP arcs We now consider principles controlling the distribution of D-sponsored LP arcs and their sponsors. The view is developed that all nonselfsponsoring LP arcs are sponsored by a certain type of support, to be fur­ ther specified presently. Before imposing PN laws to characterize LP arc D-sponsorship, it is necessary to introduce the concept Shallow Arc. A shallow arc is (i) structural, (ii) an output arc (i.e., not locally erased; see (8.89)), and (iii) unhooked, if at all, only by an Overlay arc. Recall from Chapter 5 that A unhooks B if and only if A assassinates and overlaps B ; this contrasts with zeroing, in which one arc assassi­ nates but does not overlap another: (10)

Def. 202: Shallow (arc) (A) *-* Structural (A) Λ Output arc (A) Λ (AB)(Unhook(Β,A) -> Overlay arc(B)). 5

All structural surface arcs are shallow: (11) THEOREM 127 (The Structural Surface Arc/Shallow Arc Theorem) Surface arc (A) Λ Structural (A) -» Shallow(A) . Proof. Suppose that A' is a structural surface arc. Then it follows from

the definition of "Surface Arc" that A' is not erased. A' is then an out­ put arc and not unhooked by a nonOverlay arc since not unhooked at all. QED.

4 A detailed analysis of "connected discourse" would likely reveal quasirooted LP arcs not to be self-sponsoring. If further study reveals there to be no self-sponsoring LP arcs, then, as mentioned in Chapter 4, the definition of "Logical Arc" (see Definition 66 in (4.40)) can be simplified by removing the con­ junct referring to LR arcs.

"'The specification of Overlay in the definition of "Shallow" seems natural from the viewpoint of Chapter 7. There Overlay arcs were seen to have a highly special status, one precluding them, for example, from being involved in the description of basic clause structures.

12.4. D-SPONSORED LP ARCS

557

However, not all shallow arcs are surface arcs, since shallow arcs can be foreign zeroed, like C in (12b) below, or unhooked by Overlay arcs, like D in (13b) below. Hence, they can be erased and fail to be surface arcs. To illustrate, consider (12) and (13), whose discussion follows: (12) a. French Je

Iui

parlerai.

I to him/her speak-will = "I will speak to him/her." b

LP

LP LP

Stem GR

GR'GR1

pari

er

Iui

In (12b), a PN fragment for (12a), C is a shallow 3 arc, even though it is erased by the clitic arc it sponsors, G . This is so since C is an output arc and although erased, it is not unhooked but rather zeroed. Hence, in accord with pretheoretical assumptions, the head of C is LP-Connected, via E , to node 6, the head of B and to Je, the head of A, via H . In (13b), a PN fragment for (13a), D , although erased by A , is shallow since it is an output arc and, although unhooked, it is unhooked by an Overlay arc. Thus, node 9, the head of D , is LP-Connected to,

558

12- LINEAR PRECEDENCE

(13) a. In Peoria, John saw Mary.

Top

GR x

LP

Marq LP

Loc

Ii

LP

LP saw

John

GRMary LP

e.g., nodes 10 and 11 (not all LP arcs are shown in (13b)). One significant property shared by C in (12b) and D in (13b) is that neither is a surface arc. Neither C in (12b) nor D in (13b) appears in the S-graph of its PN. Under the assumption that only heads of arcs in S-graphs are phonologically realized, the head of a shallow, nonsurface arc can have a phonologi­ cal realization only if it is also the head of some other arc which is a surface arc. Thus, e.g., the head of C in (12b), P-headed by Iui cannot, under the above assumption, have a phonological realization, since it is not the head of any surface arc. In contrast, D's head in (13b), node 9, does have a phonological realization, since it is also the head of surface arc A .

12.4. D-SPONSORED LP ARCS

559

The other significant property shared by C in (12b) and D in (13b) is that their heads are endpoints of LP arcs. Informally, both are relevant to the determination of linear precedence. Requiring the heads of certain shallow arcs to be LP-Connected is a weaker view of the principles gov­ erning LP arcs than might a priori be adopted. One might assume that only the heads of certain structural surface arcs need be LP-Connected. While this is a natural hypothesis, there is some reason to think it too strong. We consider the "shallow arc" treatment of LP arcs in section 6, basing the discussion on facts of French liaison. The pretheoretical idea here is that neighboring arcs whose heads are LP-Connected be shallow arcs. Each such LP arc would thus have as support a shallow arc. It is convenient to have a term for this special class of support relations: (14) Def. 203: Shallow Support(A l B) «-» Support(A l B)AShallow(A). For example, in (12b), C is the shallow support of E and H. In (13b), B is the shallow support of C , and J is the shallow support of K. Given these concepts and the notion LP-Triangle, defined in (15) below, one can posit The LP-Triangle Sponsor Law. This insures that each D-sponsored LP arc is sponsored by its shallow support. (15) Def. 204: LP-Triangle (A,B,C) ~ LP arc (A) Λ Shallow (B) Λ Kisses (A,B) ANeighbor (B,C) AShallow Support (C,A). (15) is read as "A, B, and C form an LP-Triangle." An LP-Triangle has the general form:

(16) where B and C are shallow arcs

A

Three arcs, A , B , and C , form an LP-Triangle if and only if A is an LP arc, C is a shallow support of A , C and B are neighbors, B kisses A , and B is shallow. We can now state:

560

12. LINEAR PRECEDENCE

(17) PN Law 98 (The LP-Triangle Sponsor Law).6 (ΉΒ) (LP-Triangle (A,B,C) «-» D-Sponsor (C,A) Λ LP arc(A). From left to right, PN law 98 says that for all A and for all C , if there is an arc B such that A, B, and C form an LP-Triangle, then C D-sponsors A , which is an LP arc. The last part of the consequent from left to right is vacuous. But it plays a crucial role from right to left where it requires for any LP arc A with a D-sponsor, C , the existence of some B such that A, B, and C form an LP-Triangle. Thus, the LP-Triangle in (16) can be further specified as in (18). Both (19), where the LP arc of an LP-Triangle is self-sponsoring, and (20), where an LP arc LP-Connects the head and tail of its shallow sponsor, are blocked by PN law 98.7

6 One might consider an alternative view of LP arc sponsorship, where both shallow colimbs of an LP-Triangle sponsor the LP arc connecting them:

While plausible, this is inconsistent with Theorem 32, The No LP Arc Successors Theorem, which insures that LP arcs cannot be successors. In (i) A is the suc­ cessor of B. Hence, to consistently permit structures like (i), one would have to complicate the definition of "Successor" so that only structural arcs with overlap­ ping D sponsors would be successors. Note that one could not simply abandon PN law 14, The LP Arc Erase Law, which permits the proof of Theorem 32· For suppose PN law 14 were rejected and that LP arcs like A in (i) were cosponsored by their overlapping shallow supports. The Successor Erase Law would determine that A erases B in (i). But since LP is not an Overlay R-sign, B would not be a shallow arc, a contradiction. Since the extra sponsor in (i) appears to serve no purpose and would cause problems, we have developed the current account of LP arc D-sponsorship in terms of shallow supports only. η

As implied in note 6, the structure:

is blocked by Theorem 32.

12.4. D-SPONSORED LP ARCS

(19)

(18)

561

(20)

B and C ate shallow arcs in (18)-(20). Since our pretheoretical view is that every pair of shallow colimbs forms an LP-Triangle with an LP arc, we add: (21) PN Law 99 (The Shallow Colimbs LP-Triangle Law) Shallow (Α Λ Β) A Colimbs (A,B)

LP-Connected (Head (A), Head (B)).

Note that PN law 99 does not specify which of the shallow colimbs is the support (and hence the sponsor) of the LP arc connecting them. The "direction" of the LP arc in question remains open. This cannot be de­ termined, in general, at the level of universal grammar. To a large extent, 8 individual grammars must specify which shallow arcs of LP-Triangles are LP arc supports. To illustrate, consider (22a, b), which differ in word order. (22) a. Yukio hit Mary. K b.

TanQnpcii^ Japanese'

Yukio

ga

Mary

ο

butta.

Yukio Nom Mary Acc hit = "Yukio hit Mary." Within the foregoing account of LP arcs, (22a, b) would have the respec­ tive structures in (23) and (24).

Q

Possibly there are certain word order universals referring to R-sign (see Pullum [l977] for some discussion in one domain). We do not deal with this ques­ tion in the present work. 9 (22b)

is from Kuno(1973a: 14).

562

12. LINEAR PRECEDENCE

(23) G>

Yukio

©

(24)

Yukio go

Mary ο

®

bulla

LP

Both (23) and (24) involve a 1 arc, A, a P arc, B , and a 2 arc, C . In both, the heads of A , B , and C are all LP-Connected. However, some of the LP-Triangles, and hence the LP sponsors, differ in the two cases. In (23), LP-Triangle (E,B,C) , while in (24), LP-Triangle (E,C,B) . In both, however, LP-Triangle (D,A,B). Thus, within certain limits, the grammars of individual languages must specify for every pair of arcs whose heads are LP-Connected which arc is the sponsor, and hence the support, of the LP arc in question. English must have a grammatical rule which specifies that, under con­ ditions X , a 2 arc, C, sponsors an LP arc, E , which LP-Connects the head of C and the head of its P arc neighbor B . In contrast, Japa­ nese needs a rule to specify that, under conditions Y , a P arc, B , spon­ sors an LP arc, E , which LP-Connects the heads of B and its 2 arc neighbor C . The grammars of individual languages, then, must in general specify the "direction" of LP arcs.

12.4. D-SPONSORED LP ARCS

563

This discussion can be made more precise by introducing the following definitions: (25) a. Def. 205: LP-Chained(A t B) LPS (a,c). (36)

pizza

John"

Since arcs like C in (36) are predictable from the "constituent mate transitivity" of LPs, they are suppressed in all of the following examples. This notationally reduces (36) to:

John

eats

pizza

To illustrate the rationale behind PN law 100, reconsider:

12.5. FURTHER CONSTRAINTS ON LP ARCS

Top

567

GRx

LP

Loc Marq

LP Peoria

LP John

LP saw GR,

LP

In (13b), all the structural arcs are shallow. Of particular interest is shallow arc D, which is assassinated by A . Even though D is not an S-graph arc, its head must, in accordance with PN law 99, be LP-Connected to the heads of all of its shallow colimbs. Thus, as shown in (13b), nodes 11 and 9 are LP-Connected by K . A and B are also shallow colimbs and hence are LP-Connected (by C ). Now, what if LPs were uniformly transitive? Since LPs (11,9) and LPs (9,10), it would follow that LPs (11,10). Requiring LPs to be transitive would force nodes 10 and 11 in (13b) to be LP-Connected by an LP arc, say N. But this would be inconsistent with other aspects of the current theory. N could not be self-sponsoring, since it would not be quasi-rooted. Hence, it would have to be sponsored by J , violating PN law 98.

568

12. LINEAR PRECEDENCE

Observe, furthermore, that 9 loose precedes 11 and 11 loose precedes 9, so that the relation Loose Precedes is not asymmetric. This is a con­ sequence of: (i) the requirement that all shallow neighbors be LP-Chained, rather than just surface arc neighbors (since D is not a surface arc, the latter choice would have precluded 9 and 11 from being LP-Connected); (ii) the nonderivational nature of PNs. All the LP arcs in a PN are present in one grammatical structure, rather than being "spread out" over a sequence of grammatical structures, as is the case with their analogues in, e.g., TG descriptions. In cases like (13b), the APG construct Loose Precedes does not match the informal notion of Linear Precedence. How­ ever, (13b) is well formed with respect to all of the PN laws so far postu­ lated which govern the distribution of LP arcs. 12.6. LP arcs and French liaison The present characterization of LP arcs permits arcs not in the S-graph of the relevant PN to sponsor LP arcs. This results because PN law 98 requires, in effect, all shallow colimbs to be LP-Chained. But shallow arcs are not necessarily surface arcs, as illustrated by C in (12b) and D in (13b) above. PN law 98 certainly imposes a weaker re­ quirement on LP arcs than might a priori be assumed adequate. One might suppose that only certain surface arcs, would sponsor LP arcs. It might seem right to restrict D-sponsoring of LP arcs to that proper subset of the class of shallow arcs which are not erased. However, this attrac­ tive position is apparently too strong. 11 ^If LP Chaining could be restricted just to surface arcs, a simpler, more elegant theory would result. Beyond facts involving liaison, the more complex account adopted here is possibly also motivated by facts considered in Kuno (1973b). In particular, the mternality constraint governing complements in English first noted in Ross (1967a) is revealed by examples cited by Kuno to be sensitive to structure distinct from that in "surface" forms. Thus, the complements in (ib) and (iib) re­ veal the same internality violations as those in (ia) and (iia). (i)

a. *1 believe that John will come is likely. b. *How likely is that John will come. (ii) a. *1 believe that John was guilty was clear to everyone. b. *Clear to everyone was that John was guilty.

12.6. LP ARCS AND FRENCH LIAISON

569

Evidence supporting the weaker position adopted here involves liaison facts in French. We quote from Selkirk (1972: III.l) the following informal description of this phenomenon: In French, there is a very general tendency to delete word-final consonants. A word in isolation is pronounced without its final consonant(s). So is a word uttered in a phrase or sentence— unless the word appears in certain syntactic contexts. In these syntactic contexts, which I will call the contexts of liaison, the final consonant of a word will delete only if the following word begins with a consonant. If it is a vowel that begins the next word, the final consonant of the first word remains. For example, in the sentence Lorenzo est petit en taille [lorsnzo ε p3ti a taj], the final /t/ of petit is lost because that word is not in a liaison context. The final /t/ of est, on the other hand, is lost only be­ cause the following word begins with a consonant. The copula est is in a liaison context, as the pronunciation of Lorenzo est un petit enfant [lorenzo et oe p3tit afa] shows. In this sentence, the final /t/ of est is pronounced. Moreover, the adjective petit is in a liaison context in this sentence and retains its /t/, the following word being vowel-initial. While we have not been able to study this area in detail, acceptance of Selkirk's data leads to the claim that shallow, rather than surface, arcs are LP-Chained. As an example, consider (38a) below and the relevant aspects of its PN, (38b). (Following Selkirk [1972], we use " cate the possibility, and "/" the impossibility, of

to indi­

liaison.) 12

(38) a. Nous donnerons/~Vune grande somme a l'UNESCO. we

give-will

a

large

amount to UNESCO =

"We will give a large amount to UNESCO."

In short, the fact that Overlay constructions like those in (ib) and (iib) make the complements final in S-graphs does not free them from the constraint. It is con­ ceivable that the restriction would be stated in APG terms through reference to shallow arcs. 12 Examples (38a), (39) and (41), including the judgments concerning liaison, and (51), excluding the liaison judgment, are from Selkirk (1972). M. Gross does not make the distinctions concerning liaison reported by Selkirk for her informants.

12. LINEAR PRECEDENCE

570 b

LP©

LP Nous

donnerons

LP une grande somme

Marq v LP a

!'UNESCO

As shown, liaison is possible in (38a) between donnerons and une. Com­ pare (39) below and its PN, (40), where liaison is also possible. (40) differs from (38) in several syntactic respects, which, however, do not affect the possibility of liaison. (39) Nous donnons/""vaux institutions charitables Ies plus chics. we

give

to institutions charitable the most fashionable =

"We give to the most fashionable institutions."

LP Nous

© donnons

UN LP

LP

αυχ

institutions charitables Ies plus chics

571

12.6. LP ARCS AND FRENCH LIAISON

In particular, in (40) 13 E 1 LP-Chains B 1 and D, while the self-erasing arc C is not LP-Chained to any arc. This accords with PN law 99, since C is

not

a shallow arc. The main point is that, while C is a final

stratum arc, it is

not

attached to an LP arc and does not influence the

possibility of liaison. Now consider (41) below, where liaison is blocked, and its PN frag­ ment, (42). (41) Nous Ia donnerons / a l'UNESCO We

her give

to the UNESCO =

"We will give it to UNESCO."

LP GRx

Stemi

LP

Nous

LP

el Ie Morq

LP !'UNESCO

We are ignoring the fact that aux is a fused form of a+ /es.

572

12. LINEAR PRECEDENCE

The significant difference between (40) and (42) is that C 1 in (42), unlike C in (40), /s a shallow arc. This follows since C 1 in (42) is structural, an output arc, and not unhooked, hence not unhooked by a nonOverlay arc. Since C 1 is shallow, its head, corresponding to elle, is LP-Connected to the heads of its shallow neighbors. In particular, C 1 1 S head is LP-Connected to 12, the head of B 2 , and to 17, the head of D . This correlates with the fact that liaison is impossible in (41). Anticipat­ ing, the possibility of liaison in cases like these appears to correlate with the "contiguity," in a sense to be made more precise below, of the relevant nodes. The relevant notion for stating where French liaison is possible is not an S-graph relation, since, apparently, nonsurface arcs like C1 in (42) influence liaison possibilities. Since liaison otherwise seems to be a phenomenon dependent upon some notion of linear contiguity, our current conclusion is that the facts attested by Selkirk bear upon how linear pre­ cedence should be characterized. We assume that the conditions for stat­ ing French liaison depend on the notion Shallow Arc, which permits defini­ tion of the directly relevant relation we call Precursor. A node a is the precursor of a node b if and only if a loose precedes b and there is no c such that a loose precedes c and c loose precedes b: (43) Def. 208: Precursor(a, b) «-> Loose Precede (a,B) Λ Not ((3c) (Loose Precede (a,c) ALoose Precede(c,b))). Because we have required shallow colimbs rather than just surface colimbs to be LP-Connected, certain nodes which are contiguous with re­ spect to S-graphs are nonetheless not related by Precursor. More precise­ ly, because of the role of shallow colimbs in LP-Connectedness, certain nodes which are related by Surface Precursor in the sense defined in the next section are not related by Precursor. In particular, this will be true of the nodes corresponding to, e.g., donnerons and a in (42). While con­ nected by Surface Precursor, these nodes are not connected by Precursor.

12.6. LP ARCS AND FRENCH LIAISON

573

If, as we suggest, the constraints on French liaison reference the notion Precursor, liaison will correctly be blocked in cases like (42). Our suggestion is that the following informal statement is a true necessary condition for liaison (for the relevant styles): (44) Necessary Condition for French Liaison Only forms corresponding to nodes which are precursors are in liai­ son contexts. That is, two words X = #··· Consonant# and Y = #Vowel ·•· # which are part of a surface string (see section 7) are in a liaison context only if X corresponds to a node a and Y to a node b such that Precursor (a,b). Thus only if node a is a precursor of node h will the italicized conso­ nant in word X have the possibility of manifesting phonetically. Our statement here must be informal, contra our usual practice, because the phenomenon in question obviously involves questions of phonological and phonetic representation, artificially ignored in the present study in which the closest we come to these matters is a recognition of a class of phono­ logical nodes corresponding to morphemes. Using " : " to indicate the contiguity of precursors, principle (44) correctly predicts the situations in (38), (40), and (42) with respect to the possibility of liaison between the italicized words, as shown in (45) and (46): (45)

Sentence a. (38) Nous : donnerons : tine grande somme : a l'UNESCO b. (40) Nous : donnons : aux : institutions ·•·

(46)

(42) Nous : la : donnerons : elle : a : l'UNESCO (liaison blocked by (44)) .

In further support of this analysis, consider (47) below—essentially the same as Selkirk's (111-39 (67))—and its PN, in (48):

12·

574

LINEAR PRECEDENCE

(47) Quells livres croit-il que nous donnerons / a Nicole? Which books think-he that we give (future) to Nicole

=

"Which books does he think that we will give to Nicole?" (48) QU GR

LBGR1 GR,

Stem GR1

Quels livres

que GR,

LP

nous LP

donnerons

LP

Marq Nicole

Of primary importance is that the 2 arc C 3 , P-headed by quels livres, is shallow. Hence, B 3 and C 3 are LP-Chained (by G), and C 3 is LP-Chainedto D (by H ) , since B 3 and. D are shallow colimbs of C 3 . Consequently, donnerons does not correspond to a precursor of the node represented by a and liaison is blocked, as shown in (49): (49) que : nous : donnerons : quels livres : a : Nicole ( liaison blocked by (44)) .

Similarly, the current analysis predicts that liaison is (indirectly) blocked by so-called Heavy NP Shift. Consider, e .g., (50) and its PN fragment (51) below:

575

12.6. LP ARCS AND FRENCH LIAISON

(50) Je donnerais / a Robert un des meilleurs livres de la collection. I give-would

to Robert one of

best

books of the collection =

"I would give to Robert one of the best books of the collection." (51) ow

GR.

LP

LP

LP donnerais

LP

© /un des\ 'meilleurs\ livres de Ia collection

Marq

LP Robert

PNs like (51) are discussed in greater detail in Chapter 13. Here, it suf­ fices that D is an Overlay arc and hence B4 is shallow. Consequently, the node corresponding to un des meilleurs livres de la collection, the head of B4, is LP-Connected to both A and C4 , both shallow colimbs of B4 . Thus, donnerais in (51) does not correspond to a precursor of the node P-headed by a and so liaison is predicted to be blocked: (52) Je : donnerais : une des meilleurs ··· : a Robert {liaison blocked by (44)). We have not been able to test this prediction with speakers sharing the other judgments given by Selkirk, who does not provide examples parallel to (50)·

576

12. LINEAR PRECEDENCE

Further support for the present approach to liaison involving appeal to shallow arcs comes from Selkirk's observation that: (53) Liaison is possible in both equi and raising constructions. This is illustrated by (54) - (56): (54) Jeanne parait

aimer Ies huitres.

Jeanne appears like (55) Elle semblait

avoir

the oysters = "Jeanne appears to like oysters.' Iu

Ies journaux.

She seemed to have read the newspapers = "She seemed to have read the newspapers." (56) Nous voulons We

want there

y

aller. go

= "We want to go there."

The relevant PN fragments for (54) and (56) are (57) and (58) respectively: (57)

Jeanne

A

aimer

Ies huitres

In (57), B , the foreign successor of H , unhooks H . Since B is not an Overlay arc, H is not a shallow arc. Hence, the head of H , P-headed by

12.6. LP ARCS AND FRENCH LIAISON

577

Jeanne, does not prevent parait and aimer from corresponding to precursors. Consequently, Jeanne does not block liaison in (57), indirectly confirming (44). (58)

voulons

y

aller

In (58), A unhooks E . Since A is not an Overlay arc, E is not a shallow arc. Hence, the head of E, P-headed by Nous, does not "inter­ vene" between voulons and y and so does not prevent liaison. Using the notation introduced above, the situation with respect to precursorhood and the possibility of liaison in (57) and (58) is summarized in (59) and (60): (59) (54) Jeanne : parait : aimer : Ies huitres. (60) (57) Nous : voulons : y : aller. Thus, with respect to conditions relevant for liaison involving Precursor­ hood, (59) and (60) predictably parallel (45a, b) and differ from (46), (49), and (52). In (59), (60), and (45a, b) the correspondents (italicized) of the relevant nodes are related by Precursor, while in (47), (50), and (53) they are not. Hence, in cases where liaison is possible, the relevant nodes are, to our knowledge, invariably linked by Precursorhood rather than mere­ ly by Surface Precursorhood, in accord with principle (44). 14 ^This account is, of course, oversimplified from the viewpoint of phonology, from which questions of word boundary deletion, etc., arise. See the discussion in section 8.

578

12. LINEAR PRECEDENCE

12.7.

Surface strings

The naive view of laymen is that sentences consist almost exclusive­ ly of strings of words. While this is a vast oversimplification, linguists seem unanimous in the view that every sentence has associated with it a string of words, and, at a more abstract level perhaps, a string of mor­ phemes. In some views, e .g., standard TG, sentences are in general asso­ ciated with more than one string. Returning to APG terms, a PN viewed independently of its LP arcs and the sponsor and erase pairs into which these enter defines no string structure. Even taking into account the LP arc apparatus, it has not yet been shown how APG notions permit the association of a string structure with PNs. More precisely, what is necessary, we assume, is to indicate minimally how each surface sentence in a PN and all of its constituents are associated with unique strings of words. A full development of this area would unquestionably require a serious treatment of phonology. While we are not prepared to enter into this domain at the moment, major steps can be taken showing how one can associate strings of phonological nodes with surface sentences. We will do this by introducing a formal definition which associates a string of phonological nodes with nontermi­ nal nodes which are node-extractable from S-graphs. Since each surface sentence is associated with a unique "maximal" nonterminal node, name­ ly, the quasi-root of the surface sentence, this effectively associates each surface sentence and each of its constituent-defining points with a string of phonological nodes. Fundamental to the possibility of associating surface strings with constituents is the question of which LP arcs are surface arcs. We have so far not given principles which determine this. Our assumption is that PN law 14, The LP Arc Erase Law and the following PN law correctly control all LP arc erasure: (61) PN Law 101 (The LP Arc Self-Erasure Law) LP arc (A) Λ Not (Self-Sponsor (A)) Λ Not ((3B) (3C) (LP-Triangle (A,B,C) ASurface arc (B aC))) -> Self-Erase(A).

579

12.7. SURFACE STRINGS

This requires every nonself-sponsoring LP arc not forming an LP-Triangle with two surface arcs to self-erase. In conjunction with The LP Arc Erase Law, this tightly limits the possibility of LP arc erasure. PN law 101 requires that the following arcs self-erase: E in (12b); K in (13); E 2 in (42); G and H in (48); and E and G in (51). The basic motivation for this law is the following. The notion Surface String will be indirectly defined in terms of nodes which bear LPs. How­ ever, not all pairs of nodes in LPs are relevant. For example, we do not want quels livres in (48) to be part of the surface string associated with the clause whose point is node 8. The correct surface string for this is obviously nous donnerons a Nicole. Informally, quels livres in (48) is positioned only to the left of croit-il in the surface string associated with (48). This result can be achieved by removing certain pairs of nodes in the LPs relation, including jdonnerons, quels livresS in (48), from the scope of the definition of "Surface String." Thus, this notion will be de­ fined in terms of nodes in the relation Surface LPs. Since donnerons and quels livres are not connected by a surface LP arc, via PN law 101, and hence are not related by Surface LPs, the latter is irrelevant to the sur­ face string associated with node 8 in (48). Surface LPs can be introduced as follows: (62) Def. 209: Surface LPs(a,b) «-» (3A)(LP arc (A) ASurface arc (A)

Λ

Govern (b,a,A)) . Thus a node a surface LPs a node b if and only if there is a surface LP arc, A , with a the head and b the tail of A . The next step toward defining "Surface String" involves the relation Surface Loose Precede. This rests, however, on the notion Surface Govern: (63) Def. 210: Surface Govern(a,b) «-* (3A)(Govern(a,b,A) λ Surface arc (A)).

580

12. LINEAR PRECEDENCE

That is, a surface governs b if and only if there is some surface arc A of which a is the head and b the tail. "Surface Loose Precede" is for­ mally defined as: (64) Def. 211: Surface Loose Precede (a, b) «-> (3c) (3d) (Surface LPs(c,d) AR-Surface Structural Govern(c,a)λR-Surface Structural Govern(d,b)). That is, one node a surface loose precedes another node b if and only if there are two nodes c and d such that (i) c surface LPs d, (ii) c R-Surface Structural Governs a, and (iii) d R-Surface Structural Governs b. To Illustrate, consider: (65)

12

ε

©

In (65), the following hold: Surface Loose Precede (8,10); Surface Loose Precede (9,10); Surface Loose Precede (9,11); Surface Loose Precede · (9,15). Further, although 17 is not LP-Connected to any nodes via a sur­ face LP arc, node 9, for example, still surface loose precedes 17. In contrast, node 16 neither surface loose precedes, nor is surface loose pre­ ceded by, any nodes since 16 does not bear the relation Surface LPs to any node nor is it R-Surface Structural governed by a node which bears Surface LPs to some node.

12.7. SURFACE STRINGS

581

The next step in defining "Surface String" is the introduction of the notion Surface Precursor, the analogue for S-graphs of the R-graph con­ cept Precursor: (66) Def. 212: Surface Precursor (a, b) «-» Surface Loose Precede (a,b)

Λ

Not ((3c) (Surface Loose Precede (a,c) ASurface Loose Precede (c,b))). We are finally in a position to define the notion Surface String (Spel­ ling) (of a Node). Informally, a sequence of concatenated phonological

nodes, P 1 + ··· + Pj c , is the surface string (spelling) of node η if and only if (i) η R-Surface Structural Governs every node in the string (con­ catenated sequence), (ii) there is no phonological node not in the string which η R-Surface Structural Governs (i.e., the string is "maximal"), and (iii) for each pair of adjacent nodes, ρ·, pj +1 , in the string, pj is the surface precursor of ρ^ +1 . As a last prequisite to defining "Surface String", we introduce the notion P(honological)-N ode Set (of a Node): (67) Def. 213: P(honological)-Node Set(X,n) Marq Closure (A) . However, it seems to us at the moment that no such general claim can be maintained. While reference to shallow arcs seems wrong for (76), there

648

13- GRAFTS, PIONEERS, AND CLOSURES

are other cases where such reference seems correct, that is, there are cases where the analogues of (71a, b) are well formed. Apparently, some flagging rules are of the general form: (80) X λ Shallow arc (A) -> Marq Closure (A). Thus, consider any of those many languages with rich case marking systems and with an analogue of English equi constructions. We illus­ trate with an example from ancient Greek (Goodwin [1965: 927]): (81) Dareios

bouletai polemikos

Darius (Nom) wants

einai.

warlike (Nom) to be =

"Darius wants to be war-like." Recall that our account of equi constructions of the English variety (see Chapter 14, section 5 for further details and contrasting varieties) in­ volves unhooking of a complement 1 arc by the upstairs self-sponsoring 1 arc. It follows that to apply this to sentences like (81) in a way con­ sistent with a Marq arc/F arc treatment of all nominal flagging, the 1 arc in the complement which overlaps the upstairs 1 arc must not have a Marq arc successor. That is, we want (81) to have a relevant structure of the form: (82)

bouletai

polemikos einai

Dareio

s

13.5. FLAG DETERMINATION

649

In (82), A unhooks arc B just as in the analogous English examples where flagging is irrelevant. Hence, although B is an output arc, it is not a tnarq closure. Therefore, the rule requiring a certain type of 1 arc in ancient Greek to be a marq closure, to guarantee flagging, cannot just refer to output arcs. It would apparently suffice for the relevant rule to reference shallow arcs. For B , although an output arc, is not a shallow arc since it is unhooked by a nonOverlay arc. 15 We conclude that in some cases rules specify that output arcs of type X must be marq closures, while in others they must say something weaker, namely that shallow arcs of type X must be marq closures. This is mild­ ly disturbing at the moment in that we do not know if there are principles (perhaps referring to R-signs, perhaps referring to the difference between case markers and prepositions/postpositions) which govern the contrast between such rules. That is, we do not know whether, e.g., the fact that (71a, b) are ill-formed in English is principled or simply an idiosyncracy. More generally, what is at issue is whether a language which has facts like (83) a. I talked to Joe. b. *1 talked Joe. could have well-formed sentences of the form: (84) a. Joe is difficult for me to talk. b. Joe is too mean for me to talk. instead of, or in addition to, those like (74). At the moment, we must leave such questions open, and hence allow individual grammars the free­ dom to have rules which require either shallow arcs or just output arcs to be marq closures. Rules like (75) and (76) only determine the existence of flagging struc­ tures for certain arc types. They do not, of course, specify the shape of F5ZI The

,

case agreement of adjectives, etc., in ancient Greek has generated a literature involving controversy about globality and related matters in TG terms, see Lakoff (1970), Andrews (1971), and Quicoli (1972). We hope in the future to show how APG provides an account of this kind of phenomenon.

650

13. GRAFTS, PIONEERS, AND CLOSURES

the required flags, nor do they distinguish between simple prepositional/ postpositional flagging cases and those involving, in our terms, the addi­ tional structure representing case markers. We will not deal with the latter matter further here. However, we would like to make a few additional remarks about the shape determination of prepositional and postpositional flags. In the simplest cases, the shape of such a flag is determined fully by the R-sign of the arc which is the predecessor of the Marq arc of which the F arc is a companion. However, even in these cases there are complications. For the actual shape is, of course, represented by a phonological node which must be the head of an L-arc. To take an example, the choice of the shape t o for a 3 flag in English involves determination of the identity of node b in a structure of the form: (85)

Joe

b What is important here is that our account has picked out the arcs relevant to determining the shape of b, as follows. D is a branch of an F arc, C, which is sponsored by a 3 arc. It will always be necessary to know, minimally, the character of the sponsor of the F arc of which the termina­ tion is a branch. Hence, to simplify the rules of relevance, we should de­ fine a notion to permit easy reference to distinct types of terminations depending on the types of the sponsors of their F arc supports. Hence:

13.5. FLAG DETERMINATION

651

(86) Def. 226: Let Prop be an arbitrary property of arcs. Then: Prop-TeTmination(A) to Termination(A).16 Of course, there are many problems in such an account, not the least of which is that the definition in (86) allows too many properties to play a role in flag shape determination. But this is an issue we cannot deal with here. 13.6. Appendix 1: Proofs Chapter 10 referred to several theorems which could only be proved with the aid of assumptions of Chapter 13. We now prove the relevant theorems. First, we consider (10.50), namely: (88) THEOREM 92 (The Ghost Arc Sponsor Theorem) Ghost(A) Λ Sponsor (3, A) > Nuclear Term arc (B). Proof. Let A' be a ghost and B' its sponsor. Assume the contrary of the consequent. It follows from Theorem 91 that B' must be a Marq arc, and of course, distinct from A'. PN law 84, The Ghost Arc Law, deter­ mines that there exists an R-successor of A' which is a facsimile of B'. Suppose C' is the R-successor in question. It follows that C' is a Marq arc and a neighbor of B'. And Theorem 130, The Marq Arc Pioneer

^See Definition 41 in (2.50).

652

13. GRAFTS, PIONEERS, AND CLOSURES

Theorem, shows that C' is a pioneer. C' and B' are distinct. If, to the contrary, they were identical, then, since C' is an R-successor of A' and hence A' an R-sponsor of C', and B' sponsors A', a contradiction of PN law 6, The Sponsor Independence Law, ensues. Therefore, B' and C' are neighboring distinct pioneers, contradicting PN law 106, The Pioneer Uniqueness Law. QED. Next, it is now obvious that (10.51) holds: (89) THEOREM 93 (The Marq Arc Status Theorem) Marq arc(A) -> Immigrant(A). Proof. Immediate from Theorem 130, The Marq Arc Pioneer Theorem and

the definition of "Pioneer." QED. Given this result and PN law 84, The Dummy Arc Law, one can make good on the earlier promise to show that every dummy arc head is a nomi­ nal, as claimed in (10.52): (90) THEOREM 94 (The Ghost Arc Head Label Theorem) Ghost(A) -> Head Label( Nom,A). Proof. Let A' be a ghost. Since A' is a graft, it is an entrant. Theorem

93 guarantees that A' is not a Marq arc, since Marq arcs are immigrants and ghosts are grafts, these being disjoint classes. Therefore, The Dummy Arc Law requires that A' be a Nuclear Term arc, hence, by the definitions, a Central arc. Therefore, PN law 29, The Central Arc Head Label Law, requires that A' be head labeled Nom, if it is not head labeled Cl. But PN law 83, The Nominal Arc Graft Head Labeling Law, specifies that Nominal arc grafts cannot be head labeled Cl. Therefore, since all Cen­ tral arcs are Nominal arcs, A' is not head labeled Cl and thus is head labeled Nom. QED. Finally, (10.53) now follows: (91) THEOREM 95 (The Dummy Arc Head Label Theorem) Dummy arc (A) -» Head Label (Nom, A) .

PROOFS

653

Proof. Immediate from Theorem 94 and the definition of "Dummy arc," which insures that every dummy arc head is a ghost arc head. QED. Hence, we have guaranteed, as desired, that all dummies are dummy nominals, and that ghost arcs give rise only to entities of this type. 13.7. Appendix 2: Weakening the Immigrant Local Sponsor Law PN law 12, The Immigrant Local Sponsor Law, requires every immi­ grant arc to have a local sponsor, hence two sponsors. In many cases, this seems motivated. However, on reflection, in many others, it seems not to be and results in otherwise unnecessary complications. The major motivation for the claim is that it permits a systematic, uniform account of immigrant arc first coordinates, via PN law 22, The Immigrant Coordinate Law. The possibility exists that PN law 12 is too strong and should be weakened to require local sponsors only for a proper subset of immigrant arcs. One possible weakening would not require this for pioneer arcs. More precisely, we might make local sponsors for immigrant arcs coexten­ sive with nonpioneer immigrants. This could be accomplished by replac­ ing PN law 12 by: (92) Potential Replacement for PN law 12 Immigrant(A) -> ((ΉΒ) (Local Sponsor(B 1 A))

V

(dans) Ies ovaires

toi

te

colie

Since the predecessor of C is a Gen arc, The APG Host Limitation Law does not say anything about cases like (ii) and, in particular, does not force B to be a Term arc.

708

14. APG RULES AND GRAMMARS

(66) a. Our rice is all high in quality. b.

•the quolity

all

our rice

Here B is an immigrant arc with G as predecessor. D is also an immi­ grant. It is unclear, however, whether B has a 1 arc local successor, with D then being a 1 arc, or whether D is a 2 arc and has a 1 arc local successor (according to the considerations of Chapter 7 involving unaccusative arcs). In either case, however, D is locally sponsored by a nonself-sponsoring arc, either the immigrant arc B , or its local suc­ cessor C. Either of these is consistent with The APG Host Limitation Law, and only these two ultimately are. 19 In our view, B is the proper local sponsor for D . This is consistent with the earlier cited entailment of the proposal that immigrant Term arc local sponsors be self-sponsoring (although not with this proposal itself), namely, that local successors not be proper local sponsors of such arc. Hence, we suspect that what is wanted is a principle strong enough to ex­ clude local successors but not strong enough to limit the class of local sponsors to self-sponsors, to allow local sponsors like B . To accomplish this, we define the new notion Constituent Starter. Where entrants are arcs with no predecessors at all, constituent starters 19The latter statements follow only from The APG Relational Succession Law, formulated in the text below.

14.6. CONDITIONS PERMITTING UNDERSPECIFICATION

709

are arcs with no local predecessors. Hence self-sponsoring arcs, grafts, and immigrant arcs fall together as constituent starters, although only members of the former two sets are entrants: (67) Def. 228: Constituent Starter(A) «-» Not((ΉΒ)(Local Predecessor(B 1 A))). We then suggest: (68) PN Law 114 (The Immigrant Term Arc Local Sponsor Law) Immigrant(A)ATerm arc (A) ALocal Sponsor (B,A) -> Constituent Starter(B) . Given (68), it is now impossible for C in (66b), even if it exists, to be a local sponsor of D . 2 0 Further, returning to (63), it is now impossible for any arc other than C to be the local sponsor of either A or B . Given the two PN laws introduced in this section, examples like (62d, e) are blocked if the multiple immigrant arcs are both Term x arcs, since this necessarily yields a contradiction of The Earliest Strata Unique­ ness Law. So far, however, the italicized conditional is not guaranteed by any explicit APG principle. We can accomplish this result by formulating a restricted version of a basic RG principle, called The Relational Succession Law, due to D. M. Perlmutter. This says, informally, that an element raised out of a term of type x(x = l,2, or 3) is of type χ in the constituent into which it is raised. This is too general to be an APG PN law as such since, e.g., it does not allow for clause union constructions, where elements are raised out of 2s to become 3s . Nor does it allow for known exceptions in which possessor elements raise out of a wide variety of constituent types to be­ come 3s , as illustrated in note 18. The Relational Succession Law can­ not hold unexceptionally for, inter alia, those cases covered by the con­ junct Not(Gen arc (B)) in the formulation of PN law 113. Hence, we propose: 20

Hie second conjunct in PN law 114 may be unnecessary. Perhaps all immi­ grant local sponsors, not only those of Term arc immigrants, are constituent starters.

710

14. APG RULES AND GRAMMARS

(69) PN Law 115 (The APG Relational Succession Law) Nominal arc (B) Λ Local Sponsor(A l B)ATerm x arc (A) A Foreign Successor(B j C)ANot(Gen arc(C)) -» Term x arc(B) . Here the third conjunct excludes clause union constructions which have U arc local sponsors for immigrants. The fifth conjunct excludes cases where an immigrant has a Gen arc predecessor. These are not covered at all by PN law 115. This law says, however, that, e.g., an immigrant suc­ cessor of a 1 arc locally sponsored by a 2 arc must be a 2 arc, etc. Referring back to (63), both A and B must now be 2 arcs, and ex­ amples like (62d,e) are fully blocked via The Earliest Strata Uniqueness Law, with the blockage mediated by The Immigrant Coordinate Law, The APG Host Limitation Law, and The Immigrant Term Arc Local Sponsor Law. One further constraint involving immigrant arcs and their local sponsors is worth mentioning. A survey of examples of these shows that, with one type of exception, every local sponsor of an immigrant arc has been an organic arc, i.e., not a graft. The exception involves pioneer arcs, treated in Chapter 13, which are by definition locally sponsored by grafts. We suggest the following restriction to render this situation lawful: (70) PN Law 116 (The Graft Local Sponsor of Immigrant Arcs Law) Local Sponsor (A,B) Almmigrant (B) AGraft (A) -» Pioneer(B) . Given PN law 116, we conjecture that it will be possible to prove that neither replacers nor ghost arcs can be the local sponsors of immigrant arcs. In any event, we are convinced that both of these must ultimately be truths of a valid APG theory. The aim of the present section has been to indicate concretely how PN laws eliminate an otherwise necessary burden from rules. By expand­ ing the set of such laws and by making them as restrictive as possible, it becomes feasible to foresee a situation in which even very complex re-

14.6. CONDITIONS PERMITTING UNDERSPECIFICATION

711

strictions in individual languages have relatively elegant formulations, because most of the complexity will have been extracted as entailments due to PN laws. We hope this view has been both illustrated and clarified by the discussions of the last two sections. 14.7. The RSign Cho and grammatical rules Chapter 8, section 1 indicated that the decision to adopt the R-Sign Cho was partially motivated by our treatment of rules. We can now elabo­ rate this comment. Suppose that, instead of positing the R-Sign Cho, one defined an arc to be a Chomeur (at c^fb)) if and only if it is a Cji Term arc with tail b which is overrun at Cj c : (71) Potential Definition of Chomeur Relation Suppose AfCj^b). Then: Chomeur (A, c^fb)) (ΉΒ) (Cj i -Overrun (B, A)) .

For example, given (71), in the following passive example, A is a Chomeur at C 2 :

Jack

(by) Maxine

(was) embarrassed

Thus, Chomeur arcs would be formally parallel to Ergative and Absolutive arcs, defined in Chapter 7. One consequence of this approach is that stratal uniqueness would have to be abandoned for all but initial strata. This, in turn, would have undesirable consequences for rules. For example, reconsider (37a), which has the partial PN:

712

14. APG RULES AND GRAMMARS

believe

(was) tickled

Joan

(by) Michael

In (73), B is, by definition, a Chomeur at C 2 . (73) causes a problem with respect to the English rule (36), namely, both A and B could be the foreign predecessors of 2 arcs without violating The Unique Eraser Law (or (36)). Ceteris paribus, (73) would, in conjunction with (36), wrongly predict that (37c) is grammatical. To circumvent this problem, one would have to add a further conjunct to the right-hand side of (36) ex­ cluding 1 arcs which are Chomeurs. As another example of the kind of problem resulting from not having the R-sign Cho, reconsider (40b), which would have the following PN under the assumptions of this section, rather than (41):

want

(to) (be) Kissed we the salamanders

14.7. THE R-SIGN CHO AND GRAMMATICAL RULES

713

The problem with (74) is that B , although a Chomeur at c 2 by defini­ tion, is a candidate for unhooking, given the statement of the English rule (45a). Ceteris paribus, (40b) would incorrectly be predicted to be gram­ matical. To preclude this, (45a) would have to be revised along the following lines: (75) Self-Sponsor(A)Al arc (A) AUnhook (Α,Β) λ X -> 1 arc(B)A Not (Chomeur (B, c final (b))). The upshot is that rules like (36) and (45a), which reference Term arcs, would have to be complicated to preclude their "applying" to Chomeur arcs. Further, given that rules like (45a) are simpler than those like (75), one would expect languages commonly to adopt the former type, and hence to treat Chomeur arcs and Term nonChomeur arcs alike. However, as previous RG work has shown, the evidence points in the other direction. It is typical that what would be Chomeurs given (71) and Term arcs are treated differently in various respects, e.g., flagging, word order, ability to "raise," "undergo equi," "trigger" reflexivization, agreement, etc. The problems with a defined Chomeur relation do not end here, how­ ever. (71) fails to cover cases of Cho arc grafts. Consider the following partial PN of a passive clause: (76)

Trixie

(was) hoodwinked

Marvin by

In (76), A, B, and C are all 1 arcs. B is a Chomeur at C 2 since A

C2

-Overruns B. However, according to the definition, A is also a

714

14. APG RULES AND GRAMMARS

Chomeur since it is overrun at C 3 by C . Moreover, C , which one wants to be a Chomeur, is not overrun and hence is not a Chomeur in any stratum. In the final stratum of (76),

C3

, C is the final 1 arc and A is a final

Chomeur arc. But these results are the opposite of those desired. As a consequence, (71) would clearly have to be altered in some way. The fact that C is not even overrun indicates that the altered definition would have to involve a disjunction. In sum, postulation of the R-Sign Cho appears, for a number of reasons, to be the best analysis.

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INDEX absolutive, 227, 231 Achenese, 245n accusative, 227, 231 Advancee Tenure Law, 379 Advancement (-Induced) Cho arc, 442 Afrikaans, 260-61, 269 Anaphoric Arc, 457 Anaphoric Arc Replacer Theorem, 457. See Theorem 102 Anaphoric Chain, 465-470-76 Anaphoric Chain First Member Theorem, 473. See Theorem 106 Anaphoric Chain First Member Char­ acterization Theorem, 474. See Theorem 107 Anaphoric Chain Law, 473. See PN Law 89 Anaphoric Link, 470 Anaphoric Pronoun, 485 Anaphoric Replacement, 457 Anaphoric Replacement Limitation Theorem, 475. See Theorem 109 Ancestral, 25 Antecedentvalid, 686 antipassive, 241-42, 343-45, 285-86, 507n APG Host Limitation Law, 706. See PN Law 113 APG Relational Succession Law, 710. See PN Law 115 Apparition, 403 arborescence, 83 Arc, 36 ARC, 75 Arc Antecedence, 456-65 Arc Antecedence Asymmetiy Theorem, 474. See Theorem 108 Arc Antecedence Intransitivity Theorem, 462. See Theorem 105

Arc Antecedent Existence Theorem, 461. See Theorem 103 Arc Antecedent Uniqueness Theorem, 461. See Theorem 104 Arc Antecedes, 452, 460 Arc Commands, 257 Arc Precede, 563 Arc Set, 77 Arc Typology Completeness Theorem, Basic, 137. See Theorem 27 Assassinate, 108 Assassination Independence Law, 505. See PN Law 93 Attached, 41 auxiliary verbs, 213, 225n Bantu, 629 Basic Arc Typology Completeness Theorem, 137. See Theorem 27 basic clause, 98 Basic Clause P Arc Continuity Law, 223. See PN Law 41 Basic Clause Predication Law, 212. See PN Law 35 Basic Clause Types, Nuclear Term Arc Determined, 239 Basic Clause Verb Existence Theorem, 220. See Theorem 53 Basic Z Constituent, 211 Basque, 343-44, 370-71, 388n Ben(efactive), 253 Binder Arc, 384 Bicircuit, 41-42 bitransitive, 246. See also ditransitive Branch, 41-42, 98 Breton, 268 Brother-in-law, 632 b-(termination), 49

INDEX

ck(A), 40

725

Companion Cosponsor Law, 607. See PN Law 104 c k (b), 231 Companion No Local Sponsor Theorem, c kK -"cW (A)> 4 0 607. See Theorem 132 l η Companionhood Uniqueness Theorem, (Α), 40 605. See Theorem 129 complementizer, 217n, 263 c^-Overrun, 287 Con Arc Endpoint Label Identity Law, c^th Stratum, 156 207. See PN Law 34 camouflage, 620-21 Conjunctive, 209 case agreement, Greek, 649n Connected, 45 Cebuano, 345 Connectedness Theorem, 54. See Central Arc Head Label Law, 200. Theorem 3 See PN Law 29 Consequentvalid, 686 Central Arc Tail Law, 258. See Constituent, 190-91 PN Law 52 Constituent, Basic Z, 211 Central RS, 197-199 Constituent Mate, 566 Chain, 81-82 Constituent Mate LPs Transitivity Chichewa, 490 Law, 566. See PN Law 100 Cho, 141, 711-14 Constituent Starter, 709 Cho Arc, 272-400 Coordinate (a), 209 Cho Arc Characterization Theorem, coordinates, 29, 149-88 442. See Theorem 101 Coordinate Sequence, 33 Cho Arc Copy Arc Seconding coordinate structures, 206-10 Theorem, 514n. See Theorem 126 Copy Arc, 114, 483 Cho Arc Cosponsor Law, 290. See Copy Arc Kernel Anaphoric Arc PN Law 60 Theorem, 486. See Theorem 111 Cho Arc No Local Successor Law, Copy Arc Theorem, 486. See 310. See PN Law 63 Theorem 110 Cho Arc Nonlogical Theorem, 348. Copy (Pronoun), 485 See Theorem 77 Core Arc Local Successor Law, 347. Cho Arc Nonself-Sponsoring See PN Law 74 Theorem, 292. See Theorem 62 Core Arc Local Successor Theorem, Cho Arc Predecessor Local Assassi­ 347. See Theorem 74 nation Theorem, 317. See Core RS, 197-199 Theorem 66 Coreferential (Anaphoric) Arc, 484 Cho Arc Second Sponsor Identity Coreferential Arc First Coordinate Law, 291. See PN Law 61 Theorem, 487. See Theorem 112 Chomeur, 272-400 Coreferential Arc Law, 487. See Chomeur Law, 295-305-309. See PN Law 90 PN Law 62 Coreferential Arc Nonpredecessor Circuit, 82, 98-101 Theorem, 703. See Theorem 134 Clan, 459 Coreferential Pronoun, 485 clause union, 123n, 212n, 221, Corpus, 678 247-48, 323-56 CORPUS LAWS, 678 Closure, 264, 611 Cosponsor, 110 Closure Law, 614. See PN Law 107 Cosponsored Domestic Arc Theorem, Colimbs, 41-42 291. See Theorem 60 compactness, 299-316 Cycle, 81-52 Compactness Candidate, 313 cyclicity, 534-41 Companion, 605

726

INDEX

D-, 106 D-R-Successor Nonc^ Arc Theorem, 435. See Theorem 96 Dead, 338-48 Dead Arc Foreign Successor Law, 347. See PN Law 72 Dead Arc Local Sponsor Law, 347. See PN Law 73 Dead Arc Nonlogical Arc Theorem, 348. See Theorem 76 Dead Arc Nonself-Sponsoring Theorem, 348. See Theorem 75 deep anaphors, 495-500 Deleted, (Node), 90 Demotion No Replacer Law, 251. See PN Law 50 Depend, 43 dependent, 35 Derivative RS, 197-199 Disjoint, 41 ditransitive, 246, 283 Domestic, 131 Domestic Cho Arc Cosponsor Nonoverlap Theorem, 293. See Theorem 64 Domestic Cho Arc Graft Spawner Theorem, 440. See Theorem 99 Domestic Nonself-Sponsoring Arc Theorem, 131. See Theorem 24 Dummy, 140, 404 Dummy Arc Head/Inexplicit Incom­ patibility Theorem, 436. See Theorem 97 Dummy Arc Head Label Theorem, 652. See Theorem 95 Dummy Arc Law, 430. See PN Law 87 dummy nominals, 401-47 Dummy Arc Overrunning Nonzeroing Theorem, 437. See Theorem 98 Dummy (Pronoun), 485 Dyirbal, 232n, 302n, 304-305

Employed Local Successor Law, 147. See PN Law 18 Endpoint, 39 Entrant, 108 equi, 469, 540-41, 648, 692-97 equi-clause-union, 331-34 Erase, 29, 60-74 Ergative, 231 Eskimo, 241-42 Evanescent, 233 Explicit, 361

Explicit (Clan), 504 Explicit Primal Clan Survivor Law, 505. See PN Law 92 extraposition, 406-407

Facsimile, 110, 406 falls through, 156 Fall-Through Final Arc Theorem, 180. See Theorem 41 Fall-Through Law, 171-174-185. See PN Law 26 F Arc Graft Theorem, 606. See Theorem 131 F Arc Law, 605. See PN Law 103 final, 69 Final arc, 179-80 Final 1 Arc Law, 228. See PN Law 44 Final Arc Nonlocal Assassination Theorem, 181. See Theorem 42 Final Arc Theorem, 182. See Theorem 43 Final Coordinate, 179 Final Stratum, 180 First arc, 180 First Coordinate, 180 First Coreferential Arc Replacee Theorem, 493. See Theorem 113 First Stratum, 180 flagging, 111-12, 602-51 Foreign, 109 Earliest Compactness Candidate, 313 Foreign Erased Final Arc Theorem, 182. See Theorem 44 Earliest Strata Uniqueness Law, 244. French, 162-63, 212n, 216n, 221, See PN Law 48 247, 277n, 285-86, 312, 323, 329, Egresser, 523 338-41, 371n, 391-93, 401, 433, Employed, 141 452-55, 489, 506-13, 557, 568-77, Employed Domestic Arc Theorem, 616-19, 647, 706n 147. See Theorem 38

INDEX

gapping, 223 GEN CORPUS, 678 GEN GRAMMAR, 678 GEN PN, 656 GEN RULE, 678 Genetic Corpus, 678 Genetic Grammar, 678 Genetic PN, 655 -656 Genetic Rule, 677 Georgian, 239-40, 241n, 307, 353-55, 371n, 416, 620-21 German, 168, 229-30, 277, 371, 391, 401, 411, 413-15, 420-24, 488 Ghost, 140, 374, 401-403-447 Ghost Arc Law, 406. See PN Law 84 Ghost Arc Broad Sponsor Theorem, 430. See Theorem 91 Ghost Arc Sponsor Theorem, 651. See Theorem 92 Ghost Arc Head Label Theorem, 652. See Theorem 94 Ghost Coordinate Law, 168. See PN Law 24 Ghost (-Induced) Cho arc, 442 Ghost Initial Coordinate Theorem, 404. See Theorem 85 Ghost/L-graph Incompatibility Theorem, 404. See Theorem 86) Ghost Sponsor Organicity Law, 428. See PN Law 86 Ghost Status Theorem, 403. See Theorem 84 GNo, 29, 211 Govern, 35, 43 governor, 35 Grammar, 678 GRAMMAR(La), 657 Grammar Law 1, Potential, 21 Grammar Law 2, Potential, 21 GRAMMAR LAWS, 678 Grammatical Termination, 49 Grammatical Termination Law, 205. See PN Law 32 GRx arc, 40 Graft, 136 Graft Assassin Law, 624. See PN Law 111 Graft Cho Arc Theorem, 441. See Theorem 100

727

Graft Coordinate Law, 169. See PN Law 25 Graft Local Sponsor of Immigrant Arcs Law, 710. See PN Law 116 Graft/Logical Arc Incompatibility Theorem, 139. See Theorem 31 Graft Nontwin Theorem, 521. See Theorem 119 Graft/Organic Arc Disjointness Theorem, 138. See Theorem 28 Graft Overlap Law, 140. See PN Law 13 Greek, 648 GRx Projection, 697

Haya, 629-31, 635, 642 Head, 35, 39 Head Label, 200 heavy NP shift, 574-75, 611-15 Host, 134 Host Limitation Law, APG, 706. See PN Law 113 Icelandic, 629, 632 Immigrant, 70-71, 132 Immigrant Coordinate Law, 159. See PN Law 22 Immigrant (-Induced) Cho arc, 442 Immigrant Intrusiveness Theorem, 295. See Theorem 25 Immigrant Local Sponsor Law, 133. See PN Law 12 Immigrant Overrun Law, 352. See PN Law 75 Immigrant Term Arc Local Sponsor Law, 709. See PN Law 114 Immigrant Unique Local Sponsor Theorem, 164. See Theorem 40 Incomplete Arc, 36 incorporation, 237 Indonesian, 697-99 Inexplicit, 361 Inexplicit Binder Arc Law, 397. See PN Law 82 initial, 69 Initial arc, 180 Initial Stratum, 180

728

INDEX

Inherent, 210 Inherent Anaphoric Arc, 483 Inherent Anaphoric Arc Seconder Law, 488. See PN Law 91 Inherent Pronoun, 485 In-Law, 632 Internal Survivor, 526 Internal Survivor Law, 526. See PN Law 94 Introduced as, 494 Intrusive, 132 inversion, 239-40, 241n, 247, 303, 307, 416-19 Island, 115, 194, 194-95n Island Law, 195n. See PN Law 58

Loc, 248n Local, 109 Local Assassination Coordinate Law, 181. See PN Law 27 Local Successor Coordinate Law, 154. See PN Law 20 Local Successor Distinct R-Sign Law, 119. See PN Law 5 Local Zeroing Law, 365. See PN Law 77 locative, 248n Logical arc, 94 Logical Arc Set, 94 Logical Arc Coordinate Theorem, 153. See Theorem 39 logical node, 89 Logical Termination, 49 Japanese, 247, 324, 561-63, 636n Logical Termination Self-Sponsor Theorem, 206. See Theorem 47 Loop, 44, 98 Kapampangan, 245n Loose Precede, 551 Kernel Anaphoric Arc, 483 Lower Pioneer, 614 Kernel Anaphoric Arc Replacee Lower Pioneer Central Arc Erasure Theorem, 502. See Successor Law, 622. See Theorem 116 PN Law 110 Kernel Pronoun, 485 Lower Pioneer/Copy Arc Incom­ Kinyarwanda, 379n patibility Theorem, 616. See Kisses, 41-42 Theorem 133 lowering, 255-258 LP Arc Erase Law, 142. See L Arc Pair Law, 144. See PN Law 14 PN Law 16 LP Arc Quasi-Root Law, 555. See L Arc Graft Law, 144. See PN Law 96 PN Law 17 LP Arc Self-Erasure Law, 578. See Lardil, 509 PN Law 101 Latin, 622-24 LP Arc Sponsor Law, 142. See Launcher, 334 PN Law 15 Launcher Law, 334. See PN Law 69 LP-Chained, 563 Launcher Successor R-Sign Law, LP-Connected, 550 346. See PN Law 71 LPs, 551 Laws, 20-21 LPs Asymmetry Theorem, 565. See left dislocation, 452-55 Theorem 128 L-graph, 91-96-97-101 LP-Triangle, 559 L-graph Root Existence Theorem, 98. LP-Triangle Sponsor Law, 560. See Theorem 5 See PN Law 98 liaison, 568-77 LR, 94-95 Lineage, 522 Linked -, 142 Linked-R-Successor Surface Arc Major, 202 Theorem, 525. See Theorem 122 Major Category Exclusiveness LNo, 29 Law, 202. See PN Law 31

729

INDEX

Mangyan, 344-45 Marq Arc Companion Law, 605. See PN Law 102 Marq Arc Law, 615. See PN Law

108

Marq Arc Pioneer Theorem, 606. See Theorem 130 Marq Arc Status Theorem, 652. See Theorem 93 Marq Closure, 628 Maximal Two P Arc Law, 218. See PN Law 37 Maximal Two Sponsor Law, 122. See PN Law 7 Mohawk, 236-37 Mojave, 215-16, 242 Mono, 686 Monovalid, 686 Motivated, 157-58 Motivated Chomage, 356 Multiple Assassin Law, 125. See PN Law 9 NL, 678, 687 Neighbor, 41 -42 Neighboring Con Arc Head Label Identity Theorem, 207. See Theorem 50 Neighboring P Arc Erase Law, 219. See PN Law 40 NO, 32 (Node) Deleted, 90 Node-Extractable, 43 Node Label, 44 No Immigrant Cho Arc Theorem, 292. See Theorem 61 No Infanticide Law, 127. See PN Law 10 No L Arc Predecessors Theorem, 145. See Theorem 36 No L Arc Successors Theorem, 144. See Theorem 35 No-LP Arc Predecessors Theorem, 143. See Theorem 33 No LP Arc Replacer/Replacee Theorem, 144. See Theorem 34 No LP Arc Successors Theorem, 143. See Theorem 32 No Mutual Sponsorship Theorem, 120. See Theorem 13

No Oblique Successors Law, 249. See PN Law 49 No Vacuous Fall-Through Law, 158. See PN Law 21 Nominals, 225-58 Nominal Arc Graft Head Labeling Law, 405. See PN Law 83 Nominal Arc Graft Law, 440. See PN Law 88 Nominal Arc Immigrant Local Sponsor Law, 706. See PN Law

112

Nominal Arc Successor Law, 257. See PN Law 51 Nominal Arc Zeroing Law, 361. See PN Law 76 Nominal RS, 197-199 nominalization, 224n Nonentrant Twin Theorem, 521. See Theorem 120 Nonnominal RS, 197-198 Nonprimary P Arc Law, 218. See PN Law 38 Nonprimary P Arc Predecessor Law, 218. See PN Law 39 Nonself-Sponsoring Entrant Theorem, 520. See Theorem 117 Nonstructural RS, 196, 198 Nonterminal Node Theorem, 53. See Theorem 2 NTNo, 29, 211 Nuclear Term Arc Stratal Continuity Law, 243. See PN Law 47 Nuclear Term RS, 197- 199 Ο, 277n, 390-96 object-raising, 420-22 Object RS1 197-199 Oblique, 248-50 Oblique x Projection, 635 Oblique RS, 197-199 Organic, 135 Organic Cho Arc Local Successor Theorem, 293. See Theorem 63 Organic Entrant Theorem, 136. See Theorem 26 Outflank, 274 Outflank Overrun Law, 367. See PN Law 78

730

INDEX

Output arc, 328 Outrank, 250 -251 Overlap, 41-42 Overlapping Self-Sponsoring UN Node-Headed Arc Theorem, 386. See Theorem 83 Overlay, 259-71 Overlay Arc Assassin Law, 271. See PN Law 57 Overlay Arc/Central Arc Nonneighbor Theorem, 262. See Theorem 58 Overlay Arc Status Law, 260. See PN Law 54 Overlay Arc Status Theorem, 261. See Theorem 56 Overlay Arc Tail/Basic Cl Node Incompatibility Theorem, 261. See Theorem 57 Overlay Arc Tail Law, 261. See PN Law 55 Overlay Arc Successor Law, 269. See PN Law 56 Overlay Arc Successor Theorem, 270. See Theorem 59 Overlay Pioneer Arc Law, 615. See PN Law 109 Overlay RS, 197-98 Overmined (Arc), 389 Overmined Arc Self-Erase Law, 389. See PN Law 81 Overrun, 241n, 274 Overrun Arc Assassination Theorem, 322. See Theorem 69 Overrun Erase Theorem, 319. See Theorem 68 Overrun Facsimile Theorem, 410. See Theorem 88 PAX, 76 PN, 101-104 PN Basic Cl Constituent Law, 259. See PN Law 53 PN(L a ), 656 PN Laws: 1 Replacer Erase Law, 24, 222-116, 130, 144, 177-78, 195n, 234, 271, 280, 322, 441, 483, 489, 502, 517-19, 524, 525, 539, 609, 610, 640

2

3

4 5 6 7

8 9 10 11 12 13 14 15 16 17 18 19 20

21

Successor Erase Law, 24, 723-116, 177-78, 195n, 234, 270-71, 317, 322, 329, 450, 517-19, 524, 525, 609, 613, 658-59 Unique Eraser Law, 24, 62, 114, 122, 177, 182, 283n, 322, 329, 333, 441, 529, 616, 687-704 Self-Sponsor Law, 24, 227-118, 121, 136, 147, 293, 348, 357, 493, 564, 606 Local Successor Distinct R-Sign Law, 24, 229, 187 Sponsor Independence Law, 24, 220, 505, 604, 652 Maximal Two Sponsor Law, 24, 122, 124, 164, 205, 224, 289, 292, 294, 334, 461-62, 486, 590, 605, 606, 619, 654 Predecessor-Replacer Spon­ sor Law, 123, 143, 486, 492, 609-10 Multiple Assassin Law, 225, 126, 327 No Infanticide Law, 63, 127 Parallel Assassin Law, 229131, 319, 450, 543, 660n Immigrant Local Sponsor Law, 24, 70-71, 233-134, 164, 292, 422n, 604, 606, 612, 653-54 Graft Overlap Law, 24, 140141, 436, 520-21, 603 LP Arc Erase Law, 242-143, 560n, 578, 597, 598 LP Arc Sponsor Law, 242143, 597 L Arc Pair Law, 244-145 L Arc Graft Law, 244-145 Employed Local Successor Law, 138-39, 147, 357 Self-Sponsor Coordinate Law, 153-154, 158, 184, 404, 436, 487, 493 Local Successor Coordinate Law, 254-155, 158, 165, 167, 168, 170, 176, 176n, 184, 314-15, 436, 515n No Vacuous Fall-Through Law, 24, 158, 167, 172, 175, 184

731

INDEX

PN Laws (cont.) 22 Immigrant Coordinate Law, 159, 167, 170, 176n, 184, 436, 607-608 23 Replacer Coordinate Law, 124n, /65-167, 176n, 184, 409n, 440, 450, 487, 515n,

610

24 Ghost Coordinate Law, 168, 176η, 184, 315, 408-409, 412, 422 25 Graft Coordinate Law, 165, /69-170, 184, 422, 565, 607, 653, 705, 710 26 Fall-Through Law, 24, 115, 130, 158, 168, 171-/74-185, 220, 224, 233, 273, 280, 282, 288, 297, 318, 322, 412, 608, 691 27 Local Assassination Coordi­ nate Law, 130-31, 176n, 181, 633n 28 P Arc Tail Label Law, 200201, 208, 217n 29 Central Arc Head Label Law, 200-205, 214, 217n, 222, 405, 652 30 P Arc Head Label Law, 201 31 Major Category Exclusiveness Law, 202, 222 32 Grammatical Termination Law, 205-206 33 Phonological Termination Law, 205-206 34 Con Arc Endpoint Label Identity Law, 207-208 35 Basic Clause Predication Law, 212, 218, 223, 327 36 Unique Primary Law, 218, 219, 224 37 Maximal Two P Arc Law, 218 38 Nonprimary P Arc Law, 218, 224 39 Nonprimary P Arc Predecessor Law, 218 40 Neighboring P Arc Erase Law, 219-220, 224, 366 41 Basic Clause P Arc Continuity Law, 223-224 42 Primary Logical Node Law, 225

PN Laws (cont.) 43 Self-Sponsoring Nuclear Term Arc Law, 226, 433, 434, 435 44 Final 1 Arc Law, 216, 228234, 238, 373, 408n, 416-18 45 Unaccusative Instability Law, 232, 238, 376 46 Unaccusative Law, 216, 235, 238, 243, 421, 512-13 47 Nuclear Term Arc Stratal Continuity Law, 243, 349-50, 416-17 48 Earliest Strata Uniqueness Law, 244, 297n, 316, 317, 356, 616, 704-705, 710 49 No Oblique Successors Law, 249, 292, 347, 512n 50 Demotion No Replacer Law, 251, 317, 357, 511-15 51 Nominal Arc Successor Law, 257 52 Central Arc Tail Law, 258259, 262, 327 53 PN Basic Cl Constituent Law, 209, 259 54 Overlay Arc Status Law,

260-261, 265, 612, 636η 55 Overlay Arc Tail Law, 261-265 56 Overlay Arc Successor Law, 269-271, 636n 57 Overlay Arc Assassin Law,

271

58 Island Law, 195n 59 Parallel L Arc Identity Law,

204n

60 Cho Arc Cosponsor Law, 290-293, 407 61 Cho Arc Second Sponsor Identity Law, 291-292, 294, 407 62 Chomeur Law, 295-305-309, 317-19, 321, 362-63, 369, 387, 407, 408n, 494, 515n 63 Cho Arc No Local Successor Law, 310, 357 64 Stratal Compactness Law, 310-3/4-316 65 Zeroing Outflank Law, 181n, 319, 366-67

732

INDEX

PN Laws (cont.) 66 U Arc Foreign Successor Law, 326, 335, 348 67 U Arc Local Sponsor Law, 326-327 68 U Arc Predecessor Branch Law, 327 69 Launcher Law, 334-335 70 Potential Launcher Erasure Law, 335 71 Launcher Successor R-Sign Law, 346 72 Dead Arc Foreign Successor Law, 347-348 73 Dead Arc Local Sponsor Law,

347 74 Core Arc Local Successor Law, 347 75 Immigrant Overrun Law, 352-356 76 Nominal Arc Zeroing Law, 327n, 361, 363-67, 382, 387, 396, 398, 407, 417, 424, 437, 504, 633n, 660n 77 Local Zeroing Law, 364-365367 78 Outflank Overrun Law, 364,

367 79 UN Node-Headed Arc Limita­ tion Law, 281-82, 363, 384387, 391, 395-96, 424 80 UN Node-Headed Arc SelfErase Law, 388 81 Overmined Arc Self-Erase Law, 336, 389-390, 624 82 Inexplicit Binder Arc Law, 397, 436 83 Nominal Arc Graft Head Labeling Law, 405, 652 84 Ghost Arc Law, 377, 406, 415-27, 435, 546, 651, 652 85 Stable Ghost Arc Sponsor Law, 377, 419, 427 86 Ghost Sponsor Organicity Law, 428, 432-33 87 Dummy Arc Law, 405, 430431, 435, 444 88 Nominal Arc Graft Law, 440441, 457 89 Anaphoric Chain Law, 473, 505, 533

PN Laws (cont.) 90 Coreferential Arc Law, 487, 489, 493, 494-95, 498-501, 542 91 Inherent Anaphoric Arc Seconder Law, 488, 493, 500-501, 536-37, 542 92 Explicit Primal Clan Survivor Law, 505-506 93 Assassination Independence Law, 364-65, 505 94 Internal Survivor Law, 24, 330n, 450, 526-545 , 694 , 702 95 Quasi-Root LP-Connectedness Law, 554-555 96 LP Arc Quasi-Root Law, 555 97 Self-Sponsoring LP Arc QuasiRoot Law, 555-556 98 LP-Triangle Sponsor Law, 560, 567 99 Shallow Colimbs LP-Triangle Law, 561, 567, 571, 592 100 Constituent Mate LPs Transi­ tivity Law, 566 101 LP Arc Self-Erasure Law, 578 102 Marq Arc Companion Law, 605, 606 103 F Arc Law, 605 104 Companion Cosponsor Law, 607, 608 105 Pioneer Neighbor Law, 608, 609 106 Pioneer Uniqueness Law, 609, 618, 652 107 Closure Law, 24, 518n, 614, 615, 616, 624 108 Marq Arc Law, 615, 619 109 Overlay Pioneer Arc Law,

615 110 Lower Pioneer Central Arc Successor Law, 622 111 Graft Assassin Law, 624 112 Nominal Arc Immigrant Local Sponsor Law, 688n, 706 113 APG Host Limitation Law, 706, 709, 710 114 Immigrant Term Arc Local Sponsor Law, 709, 710 115 APG Relational Succession Law, 708n, 710

INDEX

PN Laws (cont.) 116 Graft Local Sponsor of Immigrant Arcs Law, 710 PN LAWS, 655-656 PNo, 29 P-Node Set, 581 Pair Network, 101-104 Parallel, 41-42 Parallel Assassin Law, 129. See PN Law 11 Parallel L Arc Identity Law, 204ti. See PN Law 59 P Arc Head Label Law, 201, See PN Law 30 P Arc Tail Label Law, 200. See PN Law 28 P Arc Tail Theorem, 218. See Theorem 51 P Arc Strata! Uniqueness Theorem, 219. See Theorem 52 P Arc No Local Successor Theorem, 223-224. See Theorem 54 passive, 115, 225n, 231, 238, 241n, 272n, 303, 312, 661-65, 698; impersonal, 168, 275-76, 380n, 411, 422-25; reflexive, 308n, 390, 424-25, 488-89, 506-12; short, 125, 280, 369 Path, 81-S2 Persistent, 330 Persistent Arc Theorem, 330. See Theorem 72 PGR, 30 P-head, 68 Phonemic Node, 586 P(honological)-Node Set, 581 Phonological Termination, 49 Phonological Termination Law, 205. See PN Law 33 Pioneer (arc), 605 Pioneer Neighbor Law, 608. See PN Law 105 Pioneer Uniqueness Law, 609. See PN Law 106 Point, 47 Pointed, 47 Poltergeist, 153, 183-84 Poly, 686 Polyvalid, 686 Potential Launcher, 330 Potential Launcher Erasure Law, 335. See PN Law 70

733

Potential Grammar Law 1, 21 Potential Grammar Law 2, 21 Potentially Term Incompatible, 300 PPN, 75 Precursor, 572 Predecessor, 70, 105-106-107 Predecessor Nonsurface Arc Theorem, 116. See Theorem 8 Predecessor-Replacer Sponsor Law, 123. See PN Law 8 Predecessor Uniqueness Theorem, 294. See Theorem 65 predicates, 211-24 predicate nominal, 212-17, 220, 242, 266-67 Primal (Clan), 504 Primary, 98, 212 Primary Arc Extractable, 76 Primary Logical Node Law, 225. See PN Law 42 Primitive Arc, 34 Primitive Pair Network, 75 Pro Archood of Ghost Arcs Theorem, 545. See Theorem 125 Projection, GRx-, 697 Projection, Oblique, 635 pronominal, 278 Pro(nominal) Arc, 456 Pronominalize, 457 Pronominally Antecedes, 463 Pronoun, 485 Prop-Termination, 651 P(seudo)-head, 68 pseudo-passive, 399 Pure Seconds, 460

quantifier, 256, 382-85 quantifier floating, 135, 452-54 Quantifier Scope Suppression Convention, Universal, 26 Quasi-Root, 84, 210n, 550 Quasi-Root LP-Connectedness Law, 554. See PN Law 95 Quasi-Rooted LP arc, 550, 553-56 R-graph, 50-51-56 R-R, 36 RR, 92-94, 100 raising, 134-35, 235-36, 255-57, 433n, 451, 469, 534-37

734

INDEX

Receiver, 46 REL S, 29 Relational Succession Law, APG, 710. See PN Law 115 R(emote)-Depend, 35 R(emote)-Govern, 35 R(emote)-R, 36 reflexive, 110-11, 417-19, 534-36 reflexive passive, see passive Replace, 110 Replace Asymmetry Theorem, 121. See Theorem 15 Replace Irreflexivity Theorem, 117. See Theorem 9 Replacee, 107-12 Replacee Employed Successor Theorem, 322. See Theorem 70 Replacee Nonoverlap Theorem, 119. See Theorem 12 Replacee Nonsurface Arc Theorem, 116. See Theorem 7 Replacee Uniqueness Theorem, 125. See Theorem 20 Replacer Coordinate Law, 165. See PN Law 23 Replacer Erase Law, 112. See PN Law 1 Replacer Graft Theorem, 139. See Theorem 30 Replacer Infanticide Theorem, 127. See Theorem 23 Replacer Nonlogical Arc Theorem, 118. See Theorem 10 Replacer/Successor Incompatibility Theorem, 126. See Theorem 21 Replacer Uniqueness Theorem, 122. See Theorem 18 Reranking Law, 250-58 Restricted Stratal Continuity Theorem, 183. See Theorem 46 right dislocation, 401n, 616-19 Root, 46 RULE LAWS, 677 RULES (L a ), 656 Russian, 247, 416-19 SAX, 76 S-graph, 75-88-89-91 S-graph R-graph Theorem, 90. See Theorem 4

S-graph/R-graph Finiteness Theorem, 101. See Theorem 6 Same-Sign, 40 Second Coreferential Arc Replacee Theorem, 493. See Theorem 114 Secondary Arc Extractable, 76 Seconds, 458 Self-Erase, 64-66, 108 Self-Erasing Final Arc Theorem, 182. See Theorem 45 Se If-Sponsor, 64-66, 94 Self-Sponsor Coordinate Law, 153. See PN Law 19 Self-Sponsor Entrant Theorem, 206. See Theorem 48 Self-Sponsor Law, 117. See PN Law 4 Self-Sponsor Nonreplace Theorem, 121. See Theorem 17 Self-Sponsor Nonsuccessor Theorem, 121. See Theorem 16 Self-Sponsoring LP Arc Quasi-Root Law, 555. See PN Law 97 Self-Sponsoring Nuclear Term Arc Law, 226. See PN Law 43 Sequence, 84 Shallow (arc), 328, 556 Shallow Colimbs LP-Triangle Law, 561. See PN Law 99 Shallow Support, 559 Sign Precede, 251 Single-Rooted, 47 Sinhalese, 302n, 303-304, 307 Spanish, 229, 247, 331-34, 344n, 390-91, 393-94, 424-25 Spawns, 419n, 439 Sponsor, 29, 60-74 Sponsor Independence Law, 120. See PN Law 6 spontaneous demotion, 275, 407 Stable Dummy, 406 Stable (Ghost), 406 Stable Ghost Arc Sponsor Law, 427. See PN Law 85 Stable Ghost Overrun Theorem, 409. See Theorem 87 stranded preposition, 266, 281, 638-41 Stratal Compactness Law, 186, 310-3i4-316. See PN Law 64 Stratal Continuity, 183

735

INDEX

Family, 156 -157, 183-84 Uniqueness, 356 Uniqueness Law, 243-44 Uniqueness Theorem, 316317-323. See Theorem 55 Stratum, cfcth, 156 Structural, 84 Structural Govern, 84, 550 Structural Immigrant Arc Theorem, 146. See Theorem 37 Structural RS, 196, 198 Structural Surface Arc/Shallow Arc Theorem, 556. See Theorem 127 Successor, 69-73, 105, 106, 107 Successor Anaphoric Replacement Theorem, 497. See Theorem 115 Successor Asymmetry Theorem, 120. See Theorem 14 Successor Erase Law, 113. See PN Law 2 Successor Infanticide Theorem, 127. See Theorem 22 Successor Nonlogical Arc Theorem, 118. See Theorem 11 Successor Organic Theorem, 139. See Theorem 29 Successor Uniqueness Theorem, 123. See Theorem 19 suppletion, 145, 145n Support, 41-42 Surface Arc, 78 Surface Arc Set, 78 Surface Govern, 579 Surface Loose Precede, 580 Surface LPs, 579 Surface Precursor, 581 Surface Sentence, 85 -88 Surface String, 581 Surface Strings, 578-85 Surface Structural Govern, 550 Survivor, 504 Stratal Stratal Stratal Stratal

TAX, 76 TNo, 32 Tagalog, 213-14, 692-97 tail, 35 Tail, 39 Tail Label, 200 Temporary Chomeur Condition, 288 Term x (arc-Induced) Cho arc, 443

Term Arc Overrun Theorem, 317. See Theorem 67 Term RS, 197-199 Terminal Node/L arc Theorem, 53. See Theorem 1 Termination, 49 Termination, Prop-, 651 Termination Theorem, 206. See Theorem 49 Tertiary Arc Extractable, 76 Theorems: 1 Terminal Node/L Arc Theorem, 53 2 Nonterminal Node Theorem, 53 3 Connectedness Theorem, 54 4 S-graph R-graph Theorem, 90 5 L-graph Root Existence Theorem, 98 6 S-graph/L-graph Finiteness Theorem, 101 7 Replacee Nonsurface Arc Theorem, 116, 502 8 Predecessor Nonsurface Arc Theorem, 116, 410 9 Replace Irreflexivity Theorem, 117, 119, 121, 144 10 Replacer Nonlogical Arc Theorem, 118, 139, 141 11 Successor Nonlogieal Arc Theorem, 118 12 Replace Nonoverlap Theorem,

119 13 No Mutual Sponsorship Theorem, 120, 121 14 Successor Assymmetry Theorem, 120, 293 15 Replace Asymmetry Theorem, 121 16 Self-Sponsor Nonsuccessor Theorem, 121, 170, 206 17 Self-Sponsor Nonreplace Theorem, 121, 170 18 Replacer Uniqueness Theorem, 122, 462 19 Successor Uniqueness Theorem, 71, 123-124, 317, 334, 626, 642 20 Replacee Uniqueness Theorem, 125, 167 21 Replacer/Successor Incom­ patibility Theorem, 126, 143

736

INDEX

Theorems (cont.) 22 Successor Infanticide Theorem, 127 23 Replacer Infanticide Theorem,

127 24 Domestic Nonself-Sponsoring Arc Theorem, 131-132 25 Immigrant Intrusiveness Theorem, 133, 135, 137, 261,

295

26 Organic Entrant Theorem, 136, 139 27 Basic Arc Typology Com­ pleteness Theorem, 137-138, 171, 184 28 Graft/Organic Arc Disjointness Theorem, 138, 170, 261, 295 29 Successor Organic Theorem,

139 30 Replacer Graft Theorem, 139 31 Graft/Logical Arc Incom­ patibility Theorem, 139 32 No LP Arc Successors Theorem, 143, 146, 294, 560n, 598 33 No LP Arc Predecessors Theorem, 143-144, 294 34 No LP Arc Replacer/ Replacee Theorem, 144 35 No L Arc Successors Theorem, 144-146, 294 36 No L Arc Predecessors Theorem, 145, 294 37 Structural Immigrant Arc Theorem, 146 38 Employed Domestic Arc Theorem, 147, 289-91, 294,

606 39 Logical Arc. Coordinate Theorem, 153-154 40 Immigrant Unique Local Sponsor Theorem, 164, 167 41 Fall-Through Final Arc Theorem, iSO-182 42 Final Arc Nonlocal Assassi­ nation Theorem, 181-182 43 Final Arc Theorem, 182 44 Foreign Erased Final Arc Theorem, 182, 223

Theorems (cont.) 45 Self-Erasing Final Arc Theorem, 182, 228 46 Restricted Stratal Continuity Theorem, 183Ί84 47 Logical Termination SelfSponsor Theorem, 97, 206 48 Self-Sponsor Entrant Theorem,

206

49 Termination Theorem, 206 50 Neighboring Con Arc Head Label Identity Theorem, 207-208 51 P Arc Tail Theorem, 218, 19 52 P Arc Stratal Uniqueness Theorem, 219 53 Basic Clause Verb Existence Theorem, 220 54 P Arc No Local Successor Theorem, 223-224 55L Stratal Uniqueness Theorem, 244-45, 316-317-318-323, 356, 440, 514, 703, 704 56 Overlay Arc Status Theorem, 261 57 Overlay Arc Tail/Basic Cl Node Incompatibility Theorem, 261-262, 265, 646 58 Overlay Arc/Central Arc Nonneighbor Theorem, 262 59 Overlay Arc Successor Theorem, 270 60 Cosponsored Domestic Arc Theorem, 291, 358 61 No Immigrant Cho Arc Theorem, 292-293, 317, 358, 441, 442 62 Cho Arc Nonself-Sponsoring Theorem, 292-293, 348, 358, 441, 442 63 Organic Cho Arc Local Suc­ cessor Theorem, 293, 317 64 Domestic Cho Arc Cosponsor Nonoverlap Theorem, 293-294 65 Predecessor Uniqueness Theorem, 124, 154, 170, 294295 66 Cho Arc Predecessor Local Assassination Theorem, 288, 317-318, 322, 441 67 Term Arc Overrun Theorem, 317-318

INDEX

Theorems (cont.) 93 Marq Arc Status Theorem, 431, 652 94 Ghost Arc Head Label Theorem, 405, 431, 652-653 95 Dummy Arc Head Label Theorem, 405, 431, 652-653 96 D-R-Successor Noncj Arc Theorem, 435-436, 437 97 Dummy Arc Head/Inexplicit Incompatibility Theorem, 436-438 98 Dummy Arc Overrunning Nonzeroing Theorem, 437-438 99 Domestic Cho Arc Graft Spawner Theorem, 440 100 Graft Cho Arc Theorem, 287n, 441-442 101 Cho Arc Characterization Theorem, 442 102 Anaphoric Arc Replacer Theorem, 457, 459 103 Arc Antecedent Existence Theorem, 461, 474 349 104 Arc Antecedent Uniqueness UN Node-Headed Arc Erase Theorem, 461-462 Theorem, 369, 385-386 105 Arc Antecedence IntransiUN Node-Headed Arc Suc­ tivity Theorem, 462 cessor Theorem, 385-386 106 Anaphoric Chain First UN Node-Headed Arc Cho Arc Member Theorem, 473-474Successor Theorem, 369, 386 476 Overlapping Self-Sponsoring 107 Anaphoric Chain First Mem­ UN Node-Headed Arc Theorem, ber Characterization Theorem, 369, 386 474, 475 Ghost Status Theorem, 403108 Arc Antecedence Asymmetry 404 Theorem, 474, 476 Ghost Initial Coordinate 109 Anaphoric Replacement Theorem, 404 Limitation Theorem, 475-476, Ghost/L-graph Incompatibility 502-503 Theorem, 404 110 Copy Arc Theorem, 486, Stable Ghost Overrun Theorem, 488-92 409-410, 415, 426 111 Copy Arc Kernel Anaphoric Overrun Facsimile Theorem, Arc Theorem, 484, 486, 489 410 112 Coreferential Arc First Unstable Ghost Theorem, 410, Coordinate Theorem, 487 412-14, 427 113 First Coreferential Arc ReUnstable Ghost Nonsurface placee Theorem, 493-500, Arc Theorem, 410 508 Ghost Arc Broad Sponsor 114 Second Coreferential Arc Theorem, 430, 651 Replacee Theorem, 493 Ghost Arc Sponsor Theorem, 431, 432, 651

Theorems (cont.) 68 Overrun Erase Theorem, 283, 319, 357, 363 69 Overrun Arc Assassination Theorem, 322 70 Replacee Employed Succes­ sor Theorem, 278, 322 71 U Arc P Arc Neighbor Theorem, 327 72 Persistent Arc Theorem, 330 73 U Arc Foreign Erasure Theorem, 335 74 Core Arc Local Successor Theorem, 254, 347 75 Dead Arc Nonself-Sponsoring Theorem, 348 76 Dead Arc Nonlogical Arc Theorem, 348 77 Cho Arc Nonlogical Arc Theorem, 348 78 U Arc Nonself-Sponsoring Theorem, 348-349 79 U Arc Nonlogical Theorem, 80 81 82 83 84 85 86 87 88 89 90 91 92

737

INDEX

738 Theorems (cont.) 115 Successor Anaphoric Re­ placement Theorem, 497 116 Kernel Anaphoric Arc Replacee Erasure Theorem,

502 117 Nonself-Sponsoring Entrant Theorem, 136, 520 118 Twin Entrant Theorem, 520521 119 Graft Nontwin Theorem, 521 120 Nonentrant Twin Theorem, 521-522 121 Twin Characterization Theorem, 521-522 122 Linked-R-Successor Surface Arc Theorem, 525, 527 123 Twins Multiple Self-Erasure Theorem, 529 124 Twins Self-Erasure Theorem, 530-531 125 Pro Archood of Ghost Arcs Theorem, 545-546 126 Cho Arc Copy Arc Seconding Theorem, 514n 127 Structural Surface Arc/ Shallow Arc Theorem, 556 128 LPs Asymmetry Theorem,

Twins, 520 Twins Multiple Self-Erasure Theorem, 529. See Theorem 123 Twins Self-Erasure Theorem, 530. See Theorem 124 Types, Self-Sponsoring Term Arc Determined Clause, 246 Types, Basic Clause, Nuclear Term Arc Determined, 239

U Arc Foreign Erasure Theorem, 335. See Theorem 73 U Arc Foreign Successor Law, 326. See PN Law 66 U Arc Local Sponsor Law, 326. See PN Law 67 U Arc Nonlogical Theorem, 349. See Theorem 79 U Arc Nonself-Sponsoring Theorem, 348. See Theorem 78 U Arc P Arc Neighbor Theorem, 327. See Theorem 71 U Arc Predecessor Branch Law, 327. See PN Law 68 UN, 277n, 359-61, 367-90 UN Node-Headed Arc Cho Arc Suc­ cessor Theorem, 386. See Theorem 82 565 UN Node-Headed Arc Erase Theorem, 129 Companionhood Uniqueness 385. See Theorem 80 Theorem, 605 UN Node-Headed Arc Limitation 130 Marq Arc Pioneer Theorem, Law, 384. See PN Law 79 606, 651, 652 UN Node-Headed Self-Erase Law, 131 F Arc Graft Theorem, 606 388. See PN Law 80 132 Companion No Local UN Node-Headed Arc Successor Sponsor Theorem, 607 Theorem, 385. See Theorem 81 133 Lower Pioneer/Copy Arc Incompatibility Theorem, 616 UO, 343-45 unaccusative, 227, 374-82 134 Coreferential Arc NonpredeUnaccusative, 231 cessor Theorem, 691n, 703 Unaccusative Instability Law, 232. topicalization, 217, 266-68 See PN Law 45 tough movement, 697-99 Unaccusative Law, 235. See transitive, 227 PN Law 46 Transmitter, 46 unbounded movement, 259-71 Tree, 82-84 Undermined (Arc), 389 Turkish, 324 Twin Characterization Theorem, 521. Unergative, 231 unhooking, 125-31 See Theorem 121 Unhooks, 109 Twin Entrant Theorem, 520. See Unionizer, 349 Theorem 118

INDEX

Unique Eraser Law, 114. See PN Law 3 Unique Primary Law, 218. See PN Law 36 Unisponsored, 110 Universal Quantifier Scope Sup­ pression Convention, 26 universal rule, 238n unspecified object, 343-45 Unstable Dummy, 406 Unstable Ghost, 406 Unstable Ghost Nonsurface Arc Theorem, 410. See Theorem 90 Unstable Ghost Theorem, 410. See Theorem 89 Upper Pioneer, 614 Ur-Predecessor, 523 Ur-Successor, 523

739

VP deletion, 223 V-initial language, 213 Walbiri, 664 Well-Formed in L a , 658 Welsh, 275-76, 401 X arc, 40 Z Constituent, 191 Z Node, 192 Zeroes, 109 zeroing, 360-67 Zeroing Outflank Law, 319. See PN Law 65

Library of Congress Cataloging in Publication Data Johnson, David E 1946Arc pair grammar. Includes bibliographical references and index. 1. Grammar, Comparative and general. I. Postal, Paul M., 1936joint author. II. Title. P151.J65 415 ISBN 0-691-08270-7

80-7533